A NEW CLASS OF SMALL SUBMODULES | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 3، بهمن 2025، صفحه 157-174 اصل مقاله (176.68 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2024.13836.1777 | ||
| نویسندگان | ||
| Farkhondeh Farzalipour* 1؛ Saeed Rajaee2؛ Marzieh Poyan3 | ||
| 1Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran. | ||
| 3Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity $1\neq 0$ and $M$ a nonzero unital $R$-module. In this paper, we introduce a new notion of submodules in $M$, namely $T$-semi-annihilator small submodules of $M$ with respect to an arbitrary submodule $T$ of $M$. A submodule $N$ of $M$ is $T$-semi-annihilator small in $M$ provide that for each submodule $X$ of $M$ with $T\subseteq N+X$ implies that ${\rm Ann}(X)\ll (T:M)$. In addition, we investigate some results concerning to this new class of submodules. Among various results, we prove that for a faithful finitely generated multiplication module $M$, the submodule $N$ of $M$ is a $T$-semi-annihilator small submodule of $M$ if and only if $(N:M)$ is a $(T:M)$-semi-annihilator small ideal of $R$. Finally, we explore the properties and the behaviour of this structure under ring homomorphism, localization, direct sums and tensor product of them with a faithfully flat $R$-module. | ||
| کلیدواژهها | ||
| Small submodule؛ Semi-annihilator small submodule؛ Multiplication module | ||
| مراجع | ||
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