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A new generalization of t-lifting modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 8، شماره 1، شهریور 2020، صفحه 1-13 اصل مقاله (313.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2020.16482.1203 | ||
| نویسندگان | ||
| Y. Talebi1؛ A. R. Moniri Hamzekolaee* 2؛ M. Hosseinpour3؛ S. Asgari4 | ||
| 1University of Mazandaran, Babolsar, Iran. | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran | ||
| 3Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
| 4Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar | ||
| چکیده | ||
| In this paper we introduce the concept of $tCC$-modu\-les which is a proper generalization of ($t$-)lifting modules. Let $M$ be a module over a ring $R$. We call $M$ a $tCC$-module (related to $t$-coclosed submodules) provided that for every $t$-coclosed submodule $N$ of $M$, there exists a direct summand $K$ of $M$ such that $M=N+K$ and $N\cap K\ll K$. We prove that a module with $(D_3)$ property is $tCC$ if and only if every direct summand of $M$ is $tCC$. It is also shown that an amply supplemented module $M$ is $tCC$ if and only if $M$ decomposed to $\overline{Z}^2(M)$ and a submodule $L$ of $M$ that both of them are $tCC$. | ||
| کلیدواژه‌ها | ||
| t-small submodule؛ t-coclosed submodule؛ t-lifting module؛ tCC- module | ||
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