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 - <p style="text-align: justify;">A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R,
K +I&nbsp;≠&nbsp;R$. 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.</p>