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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Descending chain conditions for graded rings


Author: M. Saorín
Journal: Proc. Amer. Math. Soc. 115 (1992), 295-301
MSC: Primary 16W50; Secondary 16P60
MathSciNet review: 1093603
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Abstract: It is proved that if $ R$ is a perfect (resp. Artinian) strongly graded ring whose ground subring is, modulo its Jacobson radical, a finite direct product of finite-dimensional simple algebras over (nondenumerable) algebraically closed fields, then the grading group cannot contain an infinite abelian subgroup (resp. must be finite). These results extend those of A. Reid and D. S. Passman on twisted group algebras.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1093603-0
PII: S 0002-9939(1992)1093603-0
Article copyright: © Copyright 1992 American Mathematical Society