Some results on the quotient of co-m modules

	Some results on the quotient of co-m modules
Journal of Algebra and Related Topics
دوره 9، شماره 1، شهریور 2021، صفحه 79-92 اصل مقاله (303 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2021.18893.1254
نویسنده
S. Rajaee^*
Department of Mathematics, University of Payame Noor,Tehran, Iran.
چکیده
Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. In this paper, among various results, we prove that if $M$ is a cancellation $R$-module and $L$ is a nonzero simple submodule of $M$, then $L$ is a copure submodule of $M$. Moreover, in this case, if $M$ is co-m, then $M/L$ is also a co-m $R$-module. We investigate various conditions under which the quotient module $M/N$ of a co-m $M$ is also a co-m. We prove that if $M$ is a cancellation Noetherian co-m module, then for every second submodule $N$ of $M$ the quotient module $M/N$ is a co-m $R$-module. We obtain some results concerning socle and radical of co-m modules.
کلیدواژه‌ها
Comultiplication module؛ small submodule؛ quasi-copure submodule

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