Maximal quotient rings of prime group algebras
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- by John Hannah and K. C. O’Meara
- Proc. Amer. Math. Soc. 65 (1977), 1-7
- DOI: https://doi.org/10.1090/S0002-9939-1977-0573039-0
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Abstract:
It is shown that a prime nonsingular group algebra KG, where G is a group whose conjugacy classes are countable, has for its maximal right quotient ring either a full linear ring or a simple directly infinite ring. In the case where G is also locally finite only the second type can occur.References
- W. D. Burgess, Rings of quotients of group rings, Canadian J. Math. 21 (1969), 865–875. MR 244399, DOI 10.4153/CJM-1969-094-0
- Joe W. Fisher and Robert L. Snider, Prime von Neumann regular rings and primitive group algebras, Proc. Amer. Math. Soc. 44 (1974), 244–250. MR 342551, DOI 10.1090/S0002-9939-1974-0342551-9
- Edward Formanek, A problem of Passman on semisimplicity, Bull. London Math. Soc. 4 (1972), 375–376. MR 314890, DOI 10.1112/blms/4.3.375
- Edward Formanek, Maximal quotient rings of group rings, Pacific J. Math. 53 (1974), 109–116. MR 382325
- K. R. Goodearl, Prime ideals in regular self-injective rings, Canadian J. Math. 25 (1973), 829–839. MR 325690, DOI 10.4153/CJM-1973-085-3
- K. R. Goodearl, Simple regular rings and rank functions, Math. Ann. 214 (1975), 267–287. MR 409541, DOI 10.1007/BF01352109
- K. R. Goodearl and D. Handelman, Simple self-injective rings, Comm. Algebra 3 (1975), no. 9, 797–834. MR 379593, DOI 10.1080/00927877508822074
- J.-M. Goursaud and J. Valette, Anneaux de groupe héréditaires et semi-héréditaires, J. Algebra 34 (1975), 205–212 (French). MR 382410, DOI 10.1016/0021-8693(75)90178-7
- Jean-Marie Goursaud and Jacques Valette, Sur l’enveloppe injective des anneaux de groupes réguliers, Bull. Soc. Math. France 103 (1975), no. 1, 91–102 (French). MR 379569
- R. E. Johnson, Quotient rings of rings with zero singular ideal, Pacific J. Math. 11 (1961), 1385–1392. MR 143779
- Wolfgang Müller, Radikal und Sockel in Gruppenalgebren über lokalendlichen Gruppen, Arch. Math. (Basel) 25 (1974), 476–482 (German). MR 357566, DOI 10.1007/BF01238710
- Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
- Robert L. Snider, On the singular ideal of a group algebra, Comm. Algebra 4 (1976), no. 11, 1087–1089. MR 414621, DOI 10.1080/00927877608822153
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 1-7
- MSC: Primary 16A26; Secondary 16A08
- DOI: https://doi.org/10.1090/S0002-9939-1977-0573039-0
- MathSciNet review: 0573039