Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Injective and projective poset acts
Authors: L. Shahbaz
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Abstract
In this paper, after recalling the category {\bf PosAct}-$S$ of all poset acts over a pomonoid $S$; an $S$-act in the category {\bf Pos} of all posets, with action preserving monotone maps between them, some categorical properties of the category {\bf PosAct}-$S$ are considered. In particular, we describe limits and colimits such as products, coproducts, equalizers, coequalizers and etc. in this category. Also, several kinds of epimorphisms and monomorphisms are characterized in {\bf PosAct}-$S$. Finally, we study injectivity and projectivity in {\bf PosAct}-$S$ with respect to (regular) monomorphisms and (regular) epimorphisms, respectively, and see that although there is no non-trivial injective poset act with respect to monomorphisms, {\bf PosAct}-$S$ has enough regular injectives with respect to regular monomorphisms. Also, it is proved that regular injective poset acts are exactly retracts of cofree poset acts over complete posets.Department of Mathematics, University of Maragheh, Maragheh, 55181-83111 Iran
E-mail: ,
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DOI
https://doi.org/10.56415/qrs.v31.11Fulltext
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Contents
- On the intersection ideal graph of semigroups
- On topological completely inverse AG**-groupoids
- A double construction of quadratic anticenter-symmetric Jacobi-Jordan algebras
- On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography
- Semigroups in which the radical of every interior ideal is a subsemigroup
- Branched covers induced by semisymmetric quasigroup homomorphisms
- General form of the automorphism group of bicyclic graphs
- Weakly quasi invo-clean rings
- On central digraphs constructed from left loops and loops
- Some types of interior filters in quasi-ordered semigroups
- Injective and projective poset acts
