Volume 54, Issue 4
Weakly $I$-Semiregular Rings and $I$-Semiregular Rings

J. Math. Study, 54 (2021), pp. 451-459.

Published online: 2021-06

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• Abstract

Let $I$ be an ideal of a ring $R$. We call $R$ weakly $I$-semiregular if $R$/$I$ is a von Neumann regular ring. This definition generalizes $I$-semiregular rings. We give a series of characterizations and properties of this class of rings. Moreover, we also give some properties of $I$-semiregular rings.

• Keywords

Weakly $I$-semiregular rings, $I$-semiregular rings, $n$-injective modules, $n$-flat modules, ($m$,$n$)-injective modules.

16D50, 16E50

zhuzhanminzjxu@hotmail.com (Zhanmin Zhu)

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@Article{JMS-54-451, author = {Zhanmin and Zhu and zhuzhanminzjxu@hotmail.com and 16796 and Department of Mathematics, Jiaxing University, Jiaxing 314001, China and Zhanmin Zhu}, title = {Weakly $I$-Semiregular Rings and $I$-Semiregular Rings}, journal = {Journal of Mathematical Study}, year = {2021}, volume = {54}, number = {4}, pages = {451--459}, abstract = {

Let $I$ be an ideal of a ring $R$. We call $R$ weakly $I$-semiregular if $R$/$I$ is a von Neumann regular ring. This definition generalizes $I$-semiregular rings. We give a series of characterizations and properties of this class of rings. Moreover, we also give some properties of $I$-semiregular rings.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v54n4.21.09}, url = {http://global-sci.org/intro/article_detail/jms/19299.html} }
TY - JOUR T1 - Weakly $I$-Semiregular Rings and $I$-Semiregular Rings AU - Zhu , Zhanmin JO - Journal of Mathematical Study VL - 4 SP - 451 EP - 459 PY - 2021 DA - 2021/06 SN - 54 DO - http://doi.org/10.4208/jms.v54n4.21.09 UR - https://global-sci.org/intro/article_detail/jms/19299.html KW - Weakly $I$-semiregular rings, $I$-semiregular rings, $n$-injective modules, $n$-flat modules, ($m$,$n$)-injective modules. AB -

Let $I$ be an ideal of a ring $R$. We call $R$ weakly $I$-semiregular if $R$/$I$ is a von Neumann regular ring. This definition generalizes $I$-semiregular rings. We give a series of characterizations and properties of this class of rings. Moreover, we also give some properties of $I$-semiregular rings.

Zhanmin Zhu. (2021). Weakly $I$-Semiregular Rings and $I$-Semiregular Rings. Journal of Mathematical Study. 54 (4). 451-459. doi:10.4208/jms.v54n4.21.09
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