Notes on McCoy Modules
Received:April 15, 2017  Revised:December 16, 2017
Key Word: McCoy module   extension   cokernel of monomorphism   kernel of epimorphism   direct sum
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11471017), the Natural Science Foundation of Anhui Higher Education Institutions of China (Grant No.KJ2018A0304) and the Doctoral Research Foundation and the Research Culture Foundation of Anhui Normal University (Grant No.2014xmpy11).
 Author Name Affiliation Heqing ZHENG School of Mathematics and Statistics, Anhui Normal University, Anhui 241003 P. R. China Zhi CHENG School of Mathematics and Statistics, Anhui Normal University, Anhui 241003 P. R. China Xiaobin YIN School of Mathematics and Statistics, Anhui Normal University, Anhui 241003 P. R. China
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Let $R$ be a ring with an identity and $\mathcal{C}(R)$ be the category of right $R$-modules. In this paper we introduce the notion of semi-McCoy module. With this notion we show that McCoy modules of $\mathcal{C}(R)$ are closed under kernels of epimorphisms, and they are also closed under extensions and direct sums with certain conditions. We also get some results on the subcategories of McCoy modules of $\mathcal{C}(R[x])$ and $\mathcal{C}(R[x;x^{-1}])$.