On homological classification of monoids by Condition \mathbf{(P_{sc})} and new classification on Condition \mathbf{(P_{E})}

In ۱۹۹۷, Golchin and Renshaw introduced Condition (P_E) and showed that this condition implies weak flatness, although the converse is not generally valid.In this paper, we present Condition (P_{sc}) as a generalization of Condition (P_E). We also see that Condition (P_{sc}) implies weak flatness, but the converse is not necessarily true. However, for left PSF monoids the converse is holds. Moreover, we discuss some general properties and provide a homological classification of monoids by comparing Condition (P_{sc}) with some other properties.Furthermore, a new homological classification of monoids is presented by comparing Condition (P_E) with other properties.

کلیدواژه ها:

S-act ، Flatness properties ، Conditions (P_{sc}) and (P_E)