Ideals contained in subrings

Howard E. Bell*, Abraham A. Klein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Lewin has proved that if S is a ring and R a subring of finite index in S, then R contains an ideal of S which is also of finite index; and Feigelstock has recently shown that other classes of subrings must contain ideals belonging to the same class. We provide some extensions of these results, and apply them to prime rings. In the final section, we investigate finiteness of rings having only finitely many n-th powers, where n ≥ 2 is a fixed positive integer.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalHouston Journal of Mathematics
Volume24
Issue number1
StatePublished - 1998

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