On the applications of coalgebras to group algebras
HTML articles powered by AMS MathViewer
- by Alan Rosenberg
- Proc. Amer. Math. Soc. 52 (1975), 109-112
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382331-2
- PDF | Request permission
Abstract:
This paper examines the coalgebra structure on $k{[G]^ \circ }$ and relates it to the group theoretic properties of $G$. In particular it is shown that there is an intimate relation between $k[G]$ being proper and $G$ being residually finite. We use this to derive a series of conditions on the group to guarantee it being residually finite.References
- K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957), 29–62. MR 87652, DOI 10.1112/plms/s3-7.1.29
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- S. A. Jennings, The group ring of a class of infinite nilpotent groups, Canadian J. Math. 7 (1955), 169–187. MR 68540, DOI 10.4153/CJM-1955-022-5
- C. Procesi, Non commutative Jacobson-rings, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 21 (1967), 281–290. MR 224652 Alan Rosenberg, The simplicial radical of the group algebra (unpublished).
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
- Earl J. Taft, Reflexivity of algebras and coalgebras, Amer. J. Math. 94 (1972), 1111–1130. MR 309992, DOI 10.2307/2373566
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 109-112
- MSC: Primary 16A26
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382331-2
- MathSciNet review: 0382331