AIMS Mathematics (Apr 2022)

On S-principal right ideal rings

  • Jongwook Baeck

DOI
https://doi.org/10.3934/math.2022673
Journal volume & issue
Vol. 7, no. 7
pp. 12106 – 12122

Abstract

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Let S be a multiplicative subset of a ring R. A right ideal A of R is referred to as S-principal if there exist an element s∈S and a principal right ideal aR of R such that As⊆aR⊆A. A ring is referred to as an S-principal right ideal ring (S-PRIR) if every right ideal is S-principal. This paper examines S-PRIRs, which extend the notion of principal right ideal rings. Various examples, including several extensions of S-PRIRs are investigated, and some practical results are proven. A noncommutative S-PRIR that is not a principal right ideal ring is found, and the S-variants of the Eakin-Nagata-Eisenbud theorem and Cohen's theorem for S-PRIRs are proven.

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