A GENERALIZATION OF CORETRACTABLE MODULES | ||
| Journal of Algebraic Systems | ||
| مقاله 7، دوره 5، شماره 2، فروردین 2018، صفحه 163-176 اصل مقاله (198.77 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2017.5736.1287 | ||
| نویسنده | ||
| A. R. Moniri Hamzekolaee* | ||
| Department of Mathematics, University of Mazandaran, Babolsar, Iran | ||
| چکیده | ||
| Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $\overline{Z}(M)$ (for short, $\overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $\overline{Z}(M)$, there is a nonzero homomorphism $f:\dfrac{M}{N}\rightarrow M$. We investigate some conditions under which the two concepts coretractable and $\overline{Z}(M)$-coretractable, coincide. For a commutative semiperfect ring $R$, we show that $R$ is $\overline{Z}(R)$-coretractable if and only if $R$ is a Kasch ring. Some examples are provided to illustrate different concepts. | ||
| کلیدواژهها | ||
| coretractable module؛ $overline{Z}(M)$-coretractable module؛ Kasch ring | ||
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آمار تعداد مشاهده مقاله: 992 تعداد دریافت فایل اصل مقاله: 811 |
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