Some classifications of monoids by strongly idempotent cancellative $\bf (PWP)$

Articles in Press

Document Type : Research Paper

Authors

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

2 Department of mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

In this paper, we introduce Condition $(PWP_{sic})$ of acts over monoids and compare this condition with the properties left $PP$ and left $PSF$ in monoid $S$. At first we give a classification of monoids by this condition of right acts. Also, we give a classification of monoids for which some other properties of their right acts imply Condition $(PWP_{sic})$ and vice versa. Then a classification of monoids will be given for which all right Rees factor acts of $S$ satisfying some other flatness properties have Condition $(PWP_{sic})$.
The specific question of when every right $S$-act satisfying Condition $(PWP_{sic})$ has certain flatness properties or every ($GPW$-flat) $GP$-flat right $S$-act satisfies Condition $(PWP_{sic})$, have so far not been considered. In this paper, we will address these problems.

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References

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Algebraic Structures and Their Applications

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Available Online from 08 February 2025

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