Extensions of square stable range one

2014/09/13 by Huanyin Chen, Chen, Huanyin, Marjan Sheibani +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Optimization and Variational Analysis #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1409.3973

openalex publication_date 2014/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An ideal I of a ring R is square stable if aR+bR=R with a∈ I and b∈ R implies that a²+by is invertible in I for some y∈ I. We prove that an exchange ideal I of a ring R is square stable if and only if for any a∈ I, a² in J(R) implies that a∈ J(R), if and only if every regular element in I is strongly regular.

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