Affiliation:
1. Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
Abstract
We study rings [Formula: see text] which are sums of a subring [Formula: see text] and an additive subgroup [Formula: see text]. We prove that if [Formula: see text] is a prime radical ring and [Formula: see text] satisfies a polynomial identity, then [Formula: see text] is nilpotent modulo the prime radical of [Formula: see text]. Additionally, we show that if [Formula: see text] is a [Formula: see text] ring, then the prime radical of [Formula: see text] is nilpotent modulo the prime radical of [Formula: see text]. We also obtain a new condition equivalent to Koethe’s conjecture.
Funder
Bialystok University of Technology
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
3 articles.
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1. A new infinite family of
σ
-elementary rings;Communications in Algebra;2023-07-27
2. On rings which are sums of subrings and additive subgroups;International Journal of Algebra and Computation;2022-06-21
3. Note on rings which are sums of a subring and an additive subgroup;Applicable Algebra in Engineering, Communication and Computing;2021-01-06