In this paper, after recalling the category {\bf PosAct}-$S$ of all poset acts over a pomonoid $S$; an $S$-act in Pos} posets, with action preserving monotone maps between them, some categorical properties are considered. particular, we describe limits and colimits such as products, coproducts, equalizers, coequalizers etc. category. Also, several kinds epimorphisms monomorphisms characterized ...

we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non–empty set is injective in classical ZF, which arg...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.