Monoids over which products of indecomposable acts are indecomposable

Authors : Mojtaba SEDAGHATJOO, Ahmad KHAKSARİ

Pages : 229-237

View : 20 | Download : 12

Publication Date : 2017-04-01

Article Type : Research Paper

Abstract :In this paper we prove that for a monoid $S$, products of indecomposable right $S$ -acts are indecomposable if and only if $S$ contains a right zero. Besides, we prove that subacts of indecomposable right $S$ -acts are indecomposable if and only if $S$ is left reversible. Ultimately, we prove that the one element right $S$ -act $\Theta_S$ is product flat if and only if $S$ contains a left zero.
Keywords : Indecomposable act, left reversible monoid, Baer criterion, product at, super flat