TY - JOUR ID - 2473 TI - ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION (PWPsc) OF RIGHT ACTS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Mohammadzadeh Saany, Hossein AU - Nouri, Leila AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Y1 - 2023 PY - 2023 VL - 10 IS - 2 SP - 259 EP - 283 KW - S-act KW - Condition (PWPsc) KW - Flatness DO - 10.22044/jas.2022.11070.1548 N2 - 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 PSFmonoids, 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. UR - https://jas.shahroodut.ac.ir/article_2473.html L1 - https://jas.shahroodut.ac.ir/article_2473_1b05bdde687a665b7252ff249dc0f62c.pdf ER -