Year: 2013
Author: Yueming Xiang
Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19015
Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 121–130
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: $PS$-Injective module $PS$-Flat module $PS$-Coherent ring.