The maximal quotient ring of regular group rings. II
HTML articles powered by AMS MathViewer
- by Ferran Cedó PDF
- Proc. Amer. Math. Soc. 104 (1988), 357-362 Request permission
Abstract:
Let $K$ be a commutative field. Let $G$ be a locally finite group without elements of order $p$ in case char $K = p > 0$. In this paper it is proved that for some large classes of groups $G$ ($\Delta$-hypercentral, residually finite and groups satisfying Min-$q$ for all primes $q$) the Type ${{\text {I}}_\infty }$ part of the maximal quotient ring of the group ring $K[G]$ is zero.References
- Efraim P. Armendariz, Hyeng Keun Koo, and Jae Keol Park, Compressible group algebras, Comm. Algebra 13 (1985), no. 8, 1763–1777. MR 792561, DOI 10.1080/00927878508823251
- Ferran Cedó, On the maximal quotient ring of regular group rings, J. Algebra 115 (1988), no. 1, 164–174. MR 937607, DOI 10.1016/0021-8693(88)90288-8
- K. R. Goodearl, von Neumann regular rings, Monographs and Studies in Mathematics, vol. 4, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 533669
- 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, DOI 10.24033/bsmf.1794
- John Hannah, Countability in regular self-injective rings, Quart. J. Math. Oxford Ser. (2) 31 (1980), no. 123, 315–327. MR 587093, DOI 10.1093/qmath/31.3.315
- John Hannah, Ideals in regular self-injective rings and quotient rings of group algebras, Proc. London Math. Soc. (3) 42 (1981), no. 3, 533–558. MR 614733, DOI 10.1112/plms/s3-42.3.533
- John Hannah and K. C. O’Meara, Maximal quotient rings of prime group algebras, Proc. Amer. Math. Soc. 65 (1977), no. 1, 1–7. MR 573039, DOI 10.1090/S0002-9939-1977-0573039-0
- Otto H. Kegel and Bertram A. F. Wehrfritz, Locally finite groups, North-Holland Mathematical Library, Vol. 3, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. MR 0470081
- Kenneth Louden, Maximal quotient rings of ring extensions, Pacific J. Math. 62 (1976), no. 2, 489–496. MR 407059, DOI 10.2140/pjm.1976.62.489
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 357-362
- MSC: Primary 16A27; Secondary 20C07
- DOI: https://doi.org/10.1090/S0002-9939-1988-0962798-8
- MathSciNet review: 962798