Monoids over which products of indecomposable acts are indecomposable

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

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