Volume 32, Issue 1
Ore Extensions over Weakly 2-Primal Rings

Commun. Math. Res., 32 (2016), pp. 70-82.

Published online: 2021-03

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• 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.

• Keywords

$(α, δ)$-compatible ring, weakly 2-primal ring, weakly semicommutative ring, nil-semicommutative ring, Ore extension.

16S50, 16U20, 16U80

• BibTex
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• TXT
@Article{CMR-32-70, author = {Yao and Wang and and 18461 and and Yao Wang and Meimei and Jiang and and 18462 and and Meimei Jiang and Yanli and Ren and and 18463 and and Yanli Ren}, title = {Ore Extensions over Weakly 2-Primal Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.01.05}, url = {http://global-sci.org/intro/article_detail/cmr/18664.html} }
TY - JOUR T1 - Ore Extensions over Weakly 2-Primal Rings AU - Wang , Yao AU - Jiang , Meimei AU - Ren , Yanli JO - Communications in Mathematical Research VL - 1 SP - 70 EP - 82 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.01.05 UR - https://global-sci.org/intro/article_detail/cmr/18664.html KW - $(α, δ)$-compatible ring, weakly 2-primal ring, weakly semicommutative ring, nil-semicommutative ring, Ore extension. AB -

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.

Yao Wang, Meimei Jiang & Yanli Ren. (2021). Ore Extensions over Weakly 2-Primal Rings. Communications in Mathematical Research . 32 (1). 70-82. doi:10.13447/j.1674-5647.2016.01.05
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