On homological classification of monoids by Condition $\mathbf{(P_{sc})}$ and new classification on Condition $\mathbf{(P_{E})}$
نویسندگان
1 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2 Department of Mathematics Education, Farhangian University, Tehran, Iran.
3 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
doi
10.48308/cgasa.2024.234899.1472چکیده
In 1997, 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.
