Volume 29, Issue 4
Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Commun. Math. Res., 29 (2013), pp. 335-344.

Published online: 2021-05

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• Abstract

Let $R$ be a ring and $(S, ≤)$ be a strictly totally ordered monoid satisfying that $0 ≤ s$ for all $s ∈ S$. It is shown that if $λ$ is a weakly rigid homomorphism, then the skew generalized power series ring $[[R^{S,≤}, λ]]$ is right p.q.-Baer if and only if $R$ is right p.q.-Baer and any S-indexed subset of $S_r(R)$ has a generalized join in $S_r(R)$. Several known results follow as consequences of our results.

• Keywords

rings of skew generalized power series, right p.q.-Baer ring, weakly rigid endomorphism.

16W60, 16S50

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@Article{CMR-29-335, author = {Wanru and Zhang and and 18981 and and Wanru Zhang}, title = {Principal Quasi-Baerness of Rings of Skew Generalized Power Series}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {4}, pages = {335--344}, abstract = {

Let $R$ be a ring and $(S, ≤)$ be a strictly totally ordered monoid satisfying that $0 ≤ s$ for all $s ∈ S$. It is shown that if $λ$ is a weakly rigid homomorphism, then the skew generalized power series ring $[[R^{S,≤}, λ]]$ is right p.q.-Baer if and only if $R$ is right p.q.-Baer and any S-indexed subset of $S_r(R)$ has a generalized join in $S_r(R)$. Several known results follow as consequences of our results.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/18995.html} }
TY - JOUR T1 - Principal Quasi-Baerness of Rings of Skew Generalized Power Series AU - Zhang , Wanru JO - Communications in Mathematical Research VL - 4 SP - 335 EP - 344 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/18995.html KW - rings of skew generalized power series, right p.q.-Baer ring, weakly rigid endomorphism. AB -

Let $R$ be a ring and $(S, ≤)$ be a strictly totally ordered monoid satisfying that $0 ≤ s$ for all $s ∈ S$. It is shown that if $λ$ is a weakly rigid homomorphism, then the skew generalized power series ring $[[R^{S,≤}, λ]]$ is right p.q.-Baer if and only if $R$ is right p.q.-Baer and any S-indexed subset of $S_r(R)$ has a generalized join in $S_r(R)$. Several known results follow as consequences of our results.

Wanru Zhang. (2021). Principal Quasi-Baerness of Rings of Skew Generalized Power Series. Communications in Mathematical Research . 29 (4). 335-344. doi:
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