Volume 29, Issue 2
$PS$-Injective Modules, $PS$-Flat Modules and $PS$-Coherent Rings

Commun. Math. Res., 29 (2013), pp. 121-130.

Published online: 2021-05

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• Abstract

A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R, K +I ≠ R$. A ring $R$ is called left $PS$-coherent if every principally small left ideal $Ra$ is finitely presented. We develop, in this paper, $PS$-coherent rings as a generalization of $P$-coherent rings and $J$-coherent rings. To characterize $PS$-coherent rings, we first introduce $PS$-injective and $PS$-flat modules, and discuss the relation between them over some spacial rings. Some properties of left $PS$-coherent rings are also studied.

• Keywords

$PS$-Injective module, $PS$-Flat module, $PS$-Coherent ring.

16P70, 16N20, 16D10

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@Article{CMR-29-121, author = {Xiang , Yueming}, title = {$PS$-Injective Modules, $PS$-Flat Modules and $PS$-Coherent Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {2}, pages = {121--130}, abstract = {

A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R, K +I ≠ R$. A ring $R$ is called left $PS$-coherent if every principally small left ideal $Ra$ is finitely presented. We develop, in this paper, $PS$-coherent rings as a generalization of $P$-coherent rings and $J$-coherent rings. To characterize $PS$-coherent rings, we first introduce $PS$-injective and $PS$-flat modules, and discuss the relation between them over some spacial rings. Some properties of left $PS$-coherent rings are also studied.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19015.html} }
TY - JOUR T1 - $PS$-Injective Modules, $PS$-Flat Modules and $PS$-Coherent Rings AU - Xiang , Yueming JO - Communications in Mathematical Research VL - 2 SP - 121 EP - 130 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19015.html KW - $PS$-Injective module, $PS$-Flat module, $PS$-Coherent ring. AB -

A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R, K +I ≠ R$. A ring $R$ is called left $PS$-coherent if every principally small left ideal $Ra$ is finitely presented. We develop, in this paper, $PS$-coherent rings as a generalization of $P$-coherent rings and $J$-coherent rings. To characterize $PS$-coherent rings, we first introduce $PS$-injective and $PS$-flat modules, and discuss the relation between them over some spacial rings. Some properties of left $PS$-coherent rings are also studied.

Yueming Xiang. (2021). $PS$-Injective Modules, $PS$-Flat Modules and $PS$-Coherent Rings. Communications in Mathematical Research . 29 (2). 121-130. doi:
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