Quotient rings and f-radical extensions of rings

Chen Lian Chuang, Tsiu Kwen Lee, Cheng-Kai Liu

Research output: Contribution to journalArticle

Abstract

By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f (X1, . . . , Xt)is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is.

Original languageEnglish
Pages (from-to)2933-2944
Number of pages12
JournalCommunications in Algebra
Volume37
Issue number9
DOIs
Publication statusPublished - 2009 Sep 1

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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