TY - JOUR
ID - 82637
TI - On $GPW$-Flat Acts
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Rashidi, Hamideh
AU - Golchin, Akbar
AU - Mohammadzadeh Saany, Hossein
AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
AD - University of Sistan and Baluchestan
AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Y1 - 2020
PY - 2020
VL - 12
IS - 1
SP - 25
EP - 42
KW - $GPW$-flat
KW - Eventually regular monoid
KW - Eventually left almost regular monoid
DO - 10.29252/cgasa.12.1.25
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_82637.html
L1 - https://cgasa.sbu.ac.ir/article_82637_db225e4212ba0171013678302be2c9d2.pdf
ER -