Donald S. Passman:
Publications
Books
- Permutation Groups, Benjamin, New York, (1968),
[Dover, Mineola, (2012)].
- Infinite Group Rings, Marcel Dekker, New York, (1971).
- The Algebraic Structure of Group Rings,
Wiley-Interscience, New York (1977), [Krieger, Malabar, (1985)],
[Dover, Mineola, (2011)].
- Group rings, Crossed Products and Galois Theory, CBMS
Conference Notes, AMS, Providence, 1986.
- Infinite Crossed Products, Academic Press, Boston, (1989),
[Dover, Mineola, (2013)].
- A Course in Ring Theory, Wadsworth, Pacific Grove, (1991),
[Chelsea-AMS, Providence, (2004)].
- Lectures on Linear Algebra, World Scientific, Singapore, (2022).
Articles
- Nil ideals in group rings, Michigan Math. J. 9
(1962), 374-384.
- On groups with enough finite representations, Proc. AMS
14 (1963), 782-797.
- Groups with representations of bounded degree, (with I. M.
Isaacs) Canadian J. Math. 16 (1964), 299-309.
- Groups whose irreducible representations have degrees dividing
p^e, (with I. M. Isaacs) Illinois J. Math. 8 (1964),
446-457.
- The group algebras of groups of order p^4 over a modular
field, Michigan Math. J. 12 (1965), 405-415.
- Isomorphic groups and group rings, Pacific J. Math.
15 (1965), 561-583. (ibid. 43 (1972), 823-824).
- A characterization of groups in terms of the degrees of their
characters, (with I. M. Isaacs) Pacific J. Math. 15 (1965),
877-903.
- Groups whose irreducible representations have degrees dividing
p^2, Pacific J. Math. 17 (1966), 475-496.
- Character kernels of discrete groups, Proc. AMS 17
(1966), 487-492.
- A note on the action of p-groups on abelian groups, Proc.
AMS 17 (1966), 915-921.
- Groups with normal, solvable Hall p'-subgroups, Trans. AMS
123 (1966), 99-111.
- Generalized Frobenius complements, (with B. Lou) Proc. AMS
17 (1966), 1166-1172.
- Half-transitive automorphism groups, (with I. M. Isaacs)
Canadian J. Math. 18 (1966), 1243-1250.
- Solvable half-transitive automorphism groups, J. Algebra
6 (1967), 285-304.
- Solvable 3/2-transitive permutation groups, J. Algebra
7 (1967), 192-207.
- A characterization of groups in terms of the degrees of their
characters II, (with I. M. Isaacs) Pacific J. Math. 24
(1968), 467-510.
- Groups with relatively few nonlinear irreducible
characters, (with I. M. Isaacs) Canadian J. Math. 20
(1968), 1451-1458.
- On the semisimplicity of modular group algebras, Proc. AMS
20 (1969), 515-519.
- p-Solvable doubly transitive permutation groups, Pacific J.
Math. 26 (1968), 555-577.
- Some 5/2-transitive permutation groups, Pacific J. Math.
28 (1969), 157-171.
- Blocks and normal subgroups, J. Algebra 12 (1969),
569-575.
- Central idempotents in group rings, Proc. AMS 22
(1969), 555-556.
- Finite groups with small character degrees and large prime
divisors II, (with I. M. Isaacs) Pacific J. Math. 29
(1969), 311-324.
- Exceptional 3/2-transitive permutation groups, Pacific J.
Math. 29 (1969), 669-713.
- On the semisimplicity of modular group algebras II,
Canadian J. Math. 21 (1969), 1137-1145.
- Radicals of twisted group rings, Proc. London Math. Soc.
20 (1970), 409-437.
- On the semisimplicity of twisted group algebras, Proc. AMS
25 (1970), 161-166.
- Units in modular group rings, (with D. B. Coleman) Proc.
AMS 25 (1970), 510-512.
- Nonnormal subgroups of p-groups, J. Algebra 15
(1970), 352-370.
- Twisted group algebras of discrete groups, Proc. London
Math. Soc. 21 (1970), 219-231.
- Radicals of twisted group rings II, Proc. London Math. Soc.
22 (1971), 633-651.
- Linear identities in group rings, Pacific J. Math.
36 (1971), 457-483.
- Linear identities in group rings II, Pacific J. Math.
36 (1971), 485-505.
- Idempotents in group rings, Proc. AMS 28 (1971),
371-374.
- Group rings of infinite groups, Proc. Symposia in Pure
Math. 21 (1971), 117-122.
- Group rings satisfying a polynomial identity, J. Algebra
20 (1972), 103-117.
- Group rings satisfying a polynomial identity II, Pacific J.
Math. 39 (1971), 425-438.
- Minimal ideals in group rings, Proc. AMS 31 (1972),
81-86.
- Group rings satisfying a polynomial identity III, Proc. AMS
31 (1972), 87-90.
- Surgery with coefficients in a field, (with T. Petrie)
Annals of Math. 95 (1972), 385-405.
- The Jacobian of a growth transformation, Pacific J. Math.
44 (1973), 281-290.
- On the ring of quotients of a group ring, Proc. AMS
33 (1972), 221-225.
- Some isolated subsets of infinite solvable groups, Pacific
J. Math. 45 (1973), 313-319.
- On the semisimplicity of group rings of solvable groups,
(with C. R. Hampton) Trans. AMS 173 (1972), 289-301.
- On the semisimplicity of group rings of linear groups,
Pacific J. Math. 47 (1973), 221-228.
- On the semisimplicity of group rings of linear groups II,
Pacific J. Math. 48 (1973), 215-234.
- Lie solvable group rings, (with I. B. S. Passi and S.
K. Sehgal), Canadian J. Math. 25 (1973), 748-757.
- Primitive group rings, Pacific J. Math. 47 (1973),
499-506.
- A new radical for group rings?, J. Algebra 28
(1974), 556-572.
- The semisimplicity problem for group rings, Symposia Math.
13 (1974), 333-342.
- Subnormality in locally finite groups, Proc. London Math.
Soc. 28 (1974), 631-653.
- Advances in group rings, Israel J. Math. 19 (1974),
67-107.
- The type I part of a group ring, Comm. Algebra 2
(1974), 469-473.
- Radicals of group rings, Comm. Algebra 2 (1974),
295-305.
- Radical ideals in group rings of locally finite groups, J.
Algebra 33 (1975), 472-497.
- On the semisimplicity of group rings of some locally finite
groups, Pacific J. Math. 58 (1975), 179-207.
- What is a group ring?, Amer. Math. Monthly 83
(1976), 173-184.
- Group rings with simple augmentation ideals, (with K.
Bonvallet, B. Hartley and M. K. Smith) Proc. AMS 56 (1976),
79-82.
- A mechanism for describing ideals in group rings, Ring
Theory, Proceedings of Conference on Noncommutative Rings, Marcel
Dekker, New York (1977), 63-69.
- Observations on group rings, Comm. Algebra 5
(1977), 1119-1162.
- Primitive Noetherian group rings, (with D. R. Farkas) Comm.
Algebra 6 (1978), 301-315.
- The Jacobson radical of a group ring of a locally solvable
group, Proc. London Math. Soc 38 (1979), 169-192. (ibid.
39 (1979), 208-210).
- Centers and prime ideals in group algebras of
polycyclic-by-finite groups, (with M. Lorenz) J. Algebra 57
(1979), 355-386.
- Crossed products over prime rings, (with S. Montgomery)
Israel J. Math. 31 (1978), 224-256.
- Crossed products over semiprime rings, Houston J. Math.
4 (1978), 583-592.
- Prime ideals in crossed products of finite groups, (with M.
Lorenz) Israel J. Math. 33 (1979), 89-132.
- The radical of the center of a group algebra, Proc. AMS.
78 (1980), 323-326.
- Integrality and normalizing extensions of rings, (with M. Lorenz) J. Algebra
61 (1979), 289-297.
- Observations on crossed products and fixed rings, (with M.
Lorenz) Comm. Algebra 8 (1980), 743-779.
- Prime ideals in group algebras of polycyclic-by-finite
groups, (with M. Lorenz) Proc. London Math. Soc. 43 (1981),
520-543.
- Two applications of Maschke's theorem, (with M. Lorenz),
Comm. Algebra 8 (1980), 1853-1866.
- Addendum-Prime ideals in crossed products of finite groups,
(with M. Lorenz) Israel J. Math. 35 (1980), 311-322.
- Nonexistence of partial traces for group actions, (with R.
M. Guralnick and I. M. Isaacs) Rocky Mt. J. 11 (1981), 395-405.
- Units in integral group rings, (with P. F. Smith) J.
Algebra 69 (1981), 213-239.
- Fixed rings and integrality, J. Algebra 68 (1981),
510-519.
- X-Inner automorphisms of group rings, (with S. Montgomery)
Houston J. Math. 7 (1981), 395-402.
- Prime ideals in normalizing extensions, J. Algebra
73 (1981), 556-572.
- Universal fields of fractions for polycyclic group
algebras, Glasgow Math. J. 23 (1982), 103-113.
- X-Inner automorphisms of group rings II, (with S.
Montgomery) Houston J. Math. 8 (1982), 537-544.
- Nil ideals of bounded degree in group rings, Comm. Algebra
10 (1982), 1487-1495.
- It's essentially Maschke's theorem, Rocky Mt. J. 13
(1983), 37-54.
- Semiprime and prime crossed products, J. Algebra 83
(1983), 158-178.
- Galois theory of prime rings, (with S. Montgomery) J. Pure
and Appl. Algebra 31 (1984), 139-184.
- Outer Galois theory of prime rings, (with S. Montgomery)
Rocky Mt. J. 14 (1984), 305-318.
- Group rings of polycyclic groups, in "Group Theory: essays
for Philip Hall", Academic Press, London, 1984, pp. 207-257.
- The strongly prime radical of crossed products, (with M. M.
Parmenter and P. N. Stewart) Comm. Algebra 12 (1984), 1099-1113.
- Infinite crossed products and group-graded rings, Trans.
AMS 284 (1984), 707-727.
- Cancellative group-graded rings, in "Methods in Ring
Theory", Reidel, 1984, pp. 403-414.
- Semiprime crossed products, Houston J. Math. 11
(1985), 257-268.
- On the Goldie rank of group algebras, Comm. Algebra
13 (1985), 1305-1312.
- Algebraic crossed products, Contemporary Math. 43
(1985), 209-225.
- X-Inner automorphisms of crossed products and semi-invariants
of Hopf algebras, (with S. Montgomery) Israel J. Math. 55
(1986), 33-57.
- Computing the symmetric ring of quotients, J. Algebra
105 (1987), 207-235.
- Prime ideals in enveloping rings, Trans. AMS 302
(1987), 535-560.
- Prime ideals in polycyclic crossed products, Trans. AMS
301 (1987), 737-759.
- Radicals of crossed products of enveloping algebras, (with
J. Bergen and S. Montgomery) Israel J. Math. 59 (1987), 167-184.
- Prime ideals in fixed rings of free algebras, (with S.
Montgomery) Comm. Algebra 15 (1987), 2209-2234.
- Algebraic analogs of the Connes spectrum, (with S.
Montgomery) J. Algebra 115 (1988), 92-124.
- Prime ideals in restricted enveloping rings, Comm. Algebra
16 (1988), 1411-1436.
- The structure of G_0 for certain polycyclic group algebras and
related algebras, (with M. Lorenz) Contemporary
Math. 93 (1989), 283-302.
- X-inner automorphisms of enveloping rings, (with J.
Osterburg) J. Algebra 130 (1990), 277-312.
- Delta methods in enveloping rings, (with J. Bergen) J.
Algebra 133 (1990), 277-312.
- Enveloping algebras satisfying a polynomial identity, J.
Algebra 134 (1990), 469-490.
- Crossed products and enveloping algebras satisfying a
polynomial identity, Israel Math. Conf. Proc. (1989), 61-73.
- Algebraic elements in group rings, (with I. Passi) Proc.
AMS 108 (1990), 871-877.
- Skew group rings and free rings, J. Algebra 131
(1990), 502-512.
- Delta methods in enveloping algebras of Lie superalgebras,
(with J. Bergen) Trans. AMS 334 (1992), 259-280.
- Prime ideals in crossed products, in "Noncommutative
Rings", MSRI Publ. 24 (1992), 99-113.
- What makes a skew group ring prime?, (with J. Osterburg)
in "Azumaya Algebras, Actions, and Modules", Contemporary Math.
124 (1992), 165-177.
- A Connes spectrum for Hopf algebras, (with J. Osterburg and
D. Quinn) Contemporary Math. 130 (1992), 311-334.
- Delta methods in enveloping rings II, (with J. Bergen) J.
Algebra, 156 (1993), 494-534.
- Computing the Connes spectrum of a Hopf algebra, (with J.
Osterburg) Israel J. Math. 80 (1992), 225-253.
- The adjoint representation of group algebras and enveloping
algebras, Publicacions Mathematiques 36 (1992), 861-878.
- Delta methods in enveloping algebras of Lie superalgebras
II, (with J. Bergen) J. Algebra 166 (1994), 568-610.
- Semiprimitivity of group algebras of locally finite simple
groups, (with A. E. Zalesskii) Proc. London Math. Soc. 67
(1993) 243-276.
- Semiprimitivity of group algebras of locally finite groups,
in "Infinite Groups and Group Rings", World Scientific, Singapore, 1993,
pp. 77-101.
- Chains of primitive ideals, Contemporary Math. 169
(1994) 475-480.
- Semiprimitivity of group algebras of infinite simple groups of
Lie type, Proc. AMS 121 (1994) 399-403.
- The (almost) right Connes spectrum, in "Advances in Hopf
Algebras", Dekker, New York, 1994, pp. 187-203.
- Burnside's theorem for Hopf algebras, (with D. Quinn) Proc.
AMS, 123 (1995), 327-333.
- Involutory Hopf algebras, (with D. Quinn) Trans. AMS,
347 (1995), 2657-2668.
- Semiprimitivity of group algebras of locally finite groups
II, J. Pure Applied Algebra, 107 (1996), 271-302.
- Derivations of skew polynomial rings, (with J. M. Osborn),
J. Algebra, 176 (1995), 417-448.
- Semiprimitivity of group algebras: a survey, Atas da XII
Escola de Algebra, IMECC-UNICAMP, 1995, pp. 168-187.
- Delta ideals of Lie color algebras, (with J. Bergen), J.
Algebra, 177 (1995), 740-754.
- The semiprimitivity problem for group algebras of locally
finite groups, Israel J. Math., 96 (1996), 481-509.
- Representations of the Gupta-Sidki group, (with W. V.
Temple), Proc. AMS, 124 (1996), 1403-1410.
- The semiprimitivity problem for twisted group algebras of
locally finite groups, Proc. London Math. Soc. (3), 73
(1996), 323-357.
- Ultraproducts and the group ring semiprimitivity problem,
Resenhas IME-USP, 2 (1996), 253-261.
- Group algebras whose units satisfy a group identity II,
Proc. AMS, 125 (1997), 657-662.
- The Jacobson radical of group rings of locally finite
groups, Trans. AMS, 349 (1997) 4696-4751.
- Construction of free subgroups in the group of units of
modular group algebras, (with J. Z. Goncalves), Comm. Algebra,
24 (1996), 4211-4215.
- Semiprimitivity of group algebras: past results and recent
progress, in "Trends in Ring Theory", Conf. Proc. Canadian Math.
Soc. (vol. 22), AMS, Providence, 1997.
- Enveloping algebras of Lie color algebras: primeness versus
graded-primeness (with J. Bergen), Proc. AMS, 126
(1998), 1623-1635.
- Group algebras with units satisfying a
group identity II, (with Chia-Hsin Liu), Proc. AMS, 127
(1999), 337-341.
- The semiprimitivity of group algebras, in "Methods in Ring
Theory", vol. 198, Marcel Dekker, New York, 1998, pp. 199-211.
- Semi-invariants and weights of group algebras of finite
groups, (with P. Wauters), Proc. AMS, 127 (1999), 1323-1329.
- Noetherian down-up algebras, (with Ellen Kirkman and Ian
M. Musson), Proc. AMS, 127 (1999), 3161-3167.
- Simple Lie algebras of Witt type, J. Algebra, 206
(1998), 682-692.
- Simple Lie color algebras of Witt type, J. Algebra,
208 (1998), 698-721.
- Groups with all irreducible modules of finite degree, (with
W. V. Temple), in "Algebra", de Gruyter, Berlin, 2000, pp. 263--280.
- Simple Lie algebras of special type, (with J. Bergen),
J. Algebra, 227 (2000), 45-67.
- Trace methods in twisted group rings, Proc. AMS,
129 (2001), 943-946.
- Unitary units in group algebras, (with J. Z. Goncalves),
Israel J. Math., 125 (2001), 131-155.
- Invariant ideals of abelian group
algebras and representations of groups of Lie type, (with A. E.
Zalesskii), Trans. AMS, 353 (2001), 2971-2982.
- Invariant ideals of abelian group
algebras under the multiplicative action of a field, I, (with A.
E. Zalesskii), Proc. AMS, 130 (2002),
939-949.
- Invariant ideals of abelian group
algebras under the multiplicative action of a field, II, (with
J. M. Osterburg and A. E. Zalesskii), Proc. AMS, 130 (2002),
951-957.
- Free unit groups in group algebras, (with J. Z. Goncalves),
J. Algebra, 246 (2001), 226-252.
- Twisted group algebras and generalized polynomial
identities, Comm. Algebra, 29 (2001), 3683-3710.
- Polycyclic restricted Lie algebras
(with V. M. Petrogradsky), Comm. Algebra, 29 (2001), 3829-3838.
- Trace methods in twisted group rings, II, (with J. M.
Osterburg), Proc. AMS, 130 (2002), 3495-3506.
- Invariant ideals and polynomial forms, Trans. AMS,
354 (2002), 3379-3408.
- Free unit groups in algebras, (with J. Z. Goncalves),
Comm. Algebra, 31 (2003), 2219-2227.
- Invariant ideals of
abelian group algebras under the action of simple linear groups,
Resenhas IME-USP, 5 (2002), 377-390.
- Finitely generated
simple algebras: a question of B. I. Plotkin, (with A. I. Lichtman),
Israel J. Math., 143 (2004), 341-359.
- Free products in linear groups,
Proc. AMS, 132 (2004), 37-46.
- Embedding free
products in the unit group of an integral group ring,
(with J. Z. Goncalves), Archiv der Mathematik, 82 (2004), 97-102.
- Filtrations in semisimple rings, Trans. AMS, 357 (2005), 5051-5066.
- Filtrations in semisimple Lie algebras, I, (with Y.
Barnea), Trans. AMS, 358 (2006), 1983-2010.
- Filtrations in semisimple Lie algebras, II, (with Y.
Barnea), Trans. AMS, 360 (2008), 801-817.
- Linear groups and group rings, (with J. Z. Goncalves),
J. Algebra, 295 (2006), 94-118, (ibid. 307 (2007), 930-931).
- Polynomial and inverse forms, Contemporary Math., 420 (2006), 277-288.
- Prime Lie rings of derivations of commutative rings in characteristic 2,
(with Chia-Hsin Liu), J. Algebra, 311 (2007), no. 1, 352-364.
- "Multiplicative Invariant Theory" by Martin Lorenz, (book review),
Bull. AMS, 44 (2007), 157-162.
- A description of incidence rings
of group automata, (with A. V. Kelarev), Contemporary Math., 456 (2008), 27-33.
- Free subgroups in linear groups and group rings,
Contemporary Math., 456 (2008), 151-164.
- Finitary actions and invariant ideals,
Turkish J. Math., 31 (2007), 113-130.
- Involutions and free pairs of bicyclic units in integral group rings,
(with J. Z. Goncalves), J. Group Theory, 13 (2010), 721-742.
- Filtrations in semisimple Lie algebras, III, in "Advances in Ring
Theory", Birkhauser, Basel (2010), pp. 257-268.
- Multiplicative Jordan decomposition in group rings of 3-groups,
(with Chia-Hsin Liu), J. Algebra and Applications, 8 (2009), 505-519.
- Multiplicative Jordan decomposition in group rings of 2,3-groups,
(with Chia-Hsin Liu), J. Algebra and Applications, 9 (2010), 483-492.
- Invariant ideals of abelian group
algebras under the torus action of a field, I, J. Algebra,
324 (2010), 3035-3043.
- Character theory and group rings, Contemporary Math.,
524 (2010), 139-148.
- Invariant ideals of abelian group
algebras under the torus action of a field, II, J. Algebra,
331 (2011), 362-377.
- Involutions and free pairs of Bass cyclic units in integral group rings,
(with J. Z. Goncalves), J. Algebra and Applications, 10 (2011), 711-725.
- Rewritable groups,
(with M. I. Elashiry), J. Algebra, 345 (2011), 190-201.
- Elementary bialgebra properties of group rings
and enveloping rings: An introduction to Hopf algebras,
Commun. Algebra, 42 (2014), 2222-2253.
- Multiplicative Jordan decomposition in group rings of 3-groups, II,
(with Chia-Hsin Liu), Commun. Algebra, 42 (2014), 2633-2639.
- Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3,
(with Chia-Hsin Liu), J. Algebra, 388 (2013), 203-218.
- Explicit free groups in division rings
(with J. Z. Goncalves), Proc. AMS, 143 (2015), 459-468.
- Involutions and free pairs of bicyclic units in integral group rings of non-nilpotent groups,
(with J. Z. Goncalves), Proc. AMS, 143 (2015), 2395-2401.
- Groups with certain normality conditions,
(with Chia-Hsin Liu), Commun. Algebra, 44 (2016), 3308-3323.
- Free groups in normal subgroups of the multiplicative group of a division ring
(with J. Z. Goncalves), J. Algebra, 440 (2015) 128-144.
- Permutational and rewritable groups,
Proc. AMS, 147 (2019) 995-1003.
- Free pairs of symmetric elements in normal subgroups of division rings
(with J. Z. Goncalves), J. Algebra, 550 (2020) 154-185.
- Finite presentation
(with L. W. Small), Israel J. Math., 244(1) (2021) 185-214.
- On the counterexamples to the unit conjecture for group rings,
arXiv: 2108.06570v2 [math.RA] 26Aug2021.
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