On lifting acts over monoids
Subject Areas : Ring and Module Theory
B.
Tahmasebi Ashtiani
1
(Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran)
H.
Rasouli
2
(Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran)
A.
Tehranian
3
(Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran)
H.
Barzegar
4
(Department of Mathematics, Tafresh University, 39518-79611, Tafresh, Iran)
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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