Categories and General Algebraic Structures with Applications

Categories and General Algebraic Structures with Applications

On the homological classification of monoids by Condition $(G\text{-}PWP_{ssc})$ of right \(S\)-acts

Articles in Press

Document Type : Research Paper

Authors
Morteza Jafari 1
Hossein Mohammadzadeh Saany 2
1 Department of Mathematics Education, Farhangian University, Tehran, Iran
2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
10.48308/cgasa.2026.244094.1619
Abstract
Condition $(PWP_{ssc})$ introduced in (Khamechi, P., Mohammadzadeh Saany, H., Nouri, L., Classification of monoids by Condition $(PWP_{ssc})$ of right \(S\)-acts, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020), 175-197), is associated with the concept of flatness for acts over monoids. In this paper, we introduce Condition $(G\text{-}PWP_{ssc})$, which serves as a generalization of Condition $(PWP_{ssc})$. Furthermore, we demonstrate that $GP$-flat is an extension of this condition, and the converse holds for a $G$-left $PSF$ monoid. Additionally, we discuss some general properties of Condition $(G\text{-}PWP_{ssc})$ and provide a homological classification of monoids by comparing Condition $(G\text{-}PWP_{ssc})$ with some other properties.
Keywords
Condition $(G\text{-}PWP_{ssc})$
$GP$-flat
$G$-left $PSF$
Subjects
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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 11 October 2026