@article {
author = {Rashidi, Hamideh and Golchin, Akbar and Mohammadzadeh Saany, Hossein},
title = {On $GPW$-Flat Acts},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {25-42},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.25},
abstract = {In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s \in S$, there exists a natural number $n = n_ {(s, A_{S})} \in \mathbb{N}$ such that the functor $A_{S} \otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We show that a right $S$-act $A_{S}$ is $GPW$-flat if and only if for every $s \in S$ there exists a natural number $n = n_{(s, A_{S})} \in \mathbb{N}$ such that the corresponding $\varphi$ is surjective for the pullback diagram $P(Ss^n, Ss^n, \iota, \iota, S)$, where $\iota : {}_{S}(Ss^n) \rightarrow {}_{S}S$ is a monomorphism of left $S$-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa.},
keywords = {$GPW$-flat,Eventually regular monoid,Eventually left almost regular monoid},
url = {https://cgasa.sbu.ac.ir/article_82637.html},
eprint = {https://cgasa.sbu.ac.ir/article_82637_db225e4212ba0171013678302be2c9d2.pdf}
}