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

Yao Wang, Meimei Jiang & Yanli Ren

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.

  • AMS Subject Headings

16S50, 16U20, 16U80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-70, author = {Wang , YaoJiang , Meimei and Ren , Yanli}, 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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