On lifting acts over monoids

Subject Areas : Ring and Module Theory

B. Tahmasebi Ashtiani ¹ , H. Rasouli ² , A. Tehranian ³ , H. Barzegar ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran

Received: 2022-11-23 Accepted : 2022-12-27 Published : 2022-12-01

Keywords: supplement, S-act, supplemented, lifting, co-closed,

Abstract :

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.

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