Open AccessOn $ S $-principal right ideal rings
Author(s) -
Jongwook Baeck
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022673
Subject(s) - principal ideal , ideal (ethics) , mathematics , principal (computer security) , principal ideal ring , ring (chemistry) , combinatorics , discrete mathematics , law , commutative ring , computer science , political science , chemistry , commutative property , prime (order theory) , organic chemistry , operating system
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 \in S $ and a principal right ideal $ aR $ of $ R $ such that $ As \subseteq aR \subseteq 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.