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El Moussaouy, Abderrahim, Moniri Hamzekolaee, Ali Reza, Ziane, M hammed, Asgari, Samira. (1403). Investigating modules with partial endomorphisms having μ-small kernels. , 14(1), 249-262. doi: 10.22103/jmmr.2024.23354.1640
Abderrahim El Moussaouy; Ali Reza Moniri Hamzekolaee; M hammed Ziane; Samira Asgari. "Investigating modules with partial endomorphisms having μ-small kernels". , 14, 1, 1403, 249-262. doi: 10.22103/jmmr.2024.23354.1640
El Moussaouy, Abderrahim, Moniri Hamzekolaee, Ali Reza, Ziane, M hammed, Asgari, Samira. (1403). 'Investigating modules with partial endomorphisms having μ-small kernels', , 14(1), pp. 249-262. doi: 10.22103/jmmr.2024.23354.1640
El Moussaouy, Abderrahim, Moniri Hamzekolaee, Ali Reza, Ziane, M hammed, Asgari, Samira. Investigating modules with partial endomorphisms having μ-small kernels. , 1403; 14(1): 249-262. doi: 10.22103/jmmr.2024.23354.1640

Investigating modules with partial endomorphisms having μ-small kernels

Journal of Mahani Mathematical Research
دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 249-262    اصل مقاله (511.31 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23354.1640
نویسندگان
Abderrahim El Moussaouy1؛ Ali Reza Moniri Hamzekolaee* 2؛ M hammed Ziane1؛ Samira Asgari2
1Department of Mathematics, Faculty of Sciences, University of Mohammed First, Oujda, Morocco
2Department of Mathematics, University of Mazandaran, Babolsar, Iran
چکیده
In this paper, we introduce and study the concept of generalized monoform modules ($G-M$ modules, for short) which is a proper generalization of that of monoform modules. We present some of their examples, properties and characterizations. It is shown that over a commutative ring $R$, the properties monoform, small monoform, $G-M$, compressible, uniform and weakly co-Hopfian are all equivalent. Moreover, we demonstrate that a ring $R$ is an injective semisimple ring iff any $R$-module is $G-M$. Further, we prove a similar theorem to Hilbert's basis theorem for monoform, small monoform and $G-M$ modules.
کلیدواژه‌ها
Monoform modules؛ Small monoform modules؛ G-M modules
مراجع
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