arXiv subjects

Farideh Farsad

Publications and source records attributed to Farideh Farsad.

3 recordsLinked to original sources

arXiv2025

Strongly Hopfian and Co-Hopfian Acts over Monoids: Structure and Characterizations

In this paper, we introduce and explore new classes of S-acts over a monoid S, namely, strongly Hopfian and strongly co-Hopfian acts, as well as their weaker counterparts, Hopfian and co-Hopfian acts. We investigate the relationships between these newly defined structures and well-studied classes of S-acts, including Noetherian, Artinian, injective, projective, quasi-injective, and quasi-projective acts. A key result shows that, under certain conditions, a quasi-projective (respectively quasi-injective) S-act that is strongly co-Hopfian (respectively strongly Hopfian) is also strongly Hopfian (respectively strongly co-Hopfian). Moreover, we provide a variety of examples and structural results concerning the behavior of subacts and quotient acts of strongly Hopfian and strongly co-Hopfian S-acts, further elucidating the internal structure and interrelationships within this extended framework.

math.RT↗

arXiv2015

Weak Factorization System for Actions of Po-monoids on Posets

Let $S$ be a pomonoid. In this paper, {\bf Pos}-$S$, the category of $S$-posets and $S$-poset maps, is considered. One of the main aims of this paper is to draw attention to the notion of weak factorization systems in {\bf Pos}-$S.$ We show that if the identity element of $S$ is the bottom element, then $(\mathcal{C_D}, \mathcal{E_S})$ is a weak factorization system in {\bf Pos}-$S,$ where $\mathcal{C_D}$ and $\mathcal{E_S}$ are the class of down-closed embedding $S$-poset maps and the class of all split $S$-poset epimorphisms, respectively. Among other things, we use a fibrewise notion of complete posets in the category {\bf Pos}-$S/B$ under a particular case where $B$ has trivial action. We get a necessary condition for regular injective objects in {\bf Pos}-$S/B$. Finally, we characterize them under a spacial case, where $S$ is, a pogroup and conclude $(Emb, Top)$ is a weak factorization system in {\bf Pos}-$S$.

math.CT↗

arXiv2015

On the Generators in the Category of Actions of Pomonoids on Posets and its Slices

Let $S$ be a pomonoid, in this paper, {\bf Pos}-$S$, the category of $S$-posets and $S$-poset maps, is considered. First, we characterize some pomonoids on which all projectives in this category are generator or free. Then, we study regular injectivity and weakly regularly $d$-injectivity which lead to some homological classification results for pomonoids. Among other things, we get some relationships between regular injectivity in the slice category {\bf Pos}-$S/B_S$ and generators or cyclic projectives in {\bf Pos}-$S$.

math.RT↗