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Applicable Algebra in Engineering, Communication and Computing

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06-01-2021 | Original Paper

Note on rings which are sums of a subring and an additive subgroup

Author: Marek Kȩpczyk

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 3/2021

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Abstract

Let R be a ring such that \(R=R_1+R_2\), where \(R_1\) is a PI subring of R and \(R_2\) is an additive subgroup of R which satisfies a polynomial identity. We prove that if for some integer \(n\ge 1\) either \((R_1R_2)^n \subseteq R_1\) or \((R_2R_1)^n \subseteq R_1\), then R is a PI ring.

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Title: Note on rings which are sums of a subring and an additive subgroup
Author: Marek Kȩpczyk
Publication date: 06-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 3/2021
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00479-z

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