Year: 2016
Author: Yao Wang, Meimei Jiang, Yanli Ren
Communications in Mathematical Research , Vol. 32 (2016), Iss. 1 : pp. 70–82
Abstract
A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let $α$ be an endomorphism and $δ$ an $α$-derivation of a ring $R$. We prove that (1) If $R$ is an $(α, δ)$-compatible and weakly 2-primal ring, then $R[x; α, δ]$ is weakly semicommutative; (2) If $R$ is $(α, δ)$-compatible, then $R$ is weakly 2-primal if and only if $R[x; α, δ]$ is weakly 2-primal.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2016.01.05
Communications in Mathematical Research , Vol. 32 (2016), Iss. 1 : pp. 70–82
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: $(α δ)$-compatible ring weakly 2-primal ring weakly semicommutative ring nil-semicommutative ring Ore extension.