On lifting acts over monoids

Journal of Linear and Topological Algebra

دوره 11، شماره 04، اسفند 2022، صفحه 265-269   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.699063

نویسندگان

B. Tahmasebi Ashtiani¹؛ H. Rasouli^{* 1}؛ A. Tehranian¹؛ H. Barzegar²

¹Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

²Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran

چکیده

Let $A$ be an $S$-act where $S$ is a monoid. Then $A$ is called lifting if every proper subact $L$ of $A$ lies over a direct summand, that is, $L$ contains a direct summand $K$ of $A$ such that $K\subset L$ is co-small in $A$. In this paper, characterizations of lifting $S$-acts and co-closed subacts are presented. We show that the class of supplemented acts are strictly larger than that of lifting ones.
 

کلیدواژه‌ها

S-act؛ supplement؛ supplemented؛ lifting؛ co-closed

مراجع

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