Document Type : Original Manuscript

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

In this paper, we introduce Condition (PWPsc) as a generalization of Condition (PWP_E) of acts over monoids, and we observe that Condition (PWPsc) does not imply Condition (PWP_E). In general, we show that Condition (PWPsc) implies the property of being principally weakly flat, and that in left PSF
monoids, the converse of this implication is also true. Moreover, we present some general properties and a homological classification of monoids by comparing Condition (PWPsc) with some other properties. Finally, we describe left PSF monoids for which S^I_S satisfies Condition (PWPsc) for any nonempty set I.

Keywords

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