H. Barzegar
Department of Mathematics, Tafresh university, Tafresh, Iran.
[ 1 ] - Po-S-Dense Monomorphism
In this paper we take $mathcal A$ to be the category {bf Pos-S} of $S$-posets, for a posemigroup $S$, ${mathcal M}_{pd}$ to be the class of partially ordered sequantially-dense monomorphisms and study the categorical properties, such as limits and colimits, of this class. These properties are usually needed to study the homological notions, such as injectivity, of $S$-...
[ 2 ] - SEQUENTIALLY COMPACT S-ACTS
The investigation of equational compactness was initiated by Banaschewski and Nelson. They proved that pure injectivity is equivalent to equational compactness. Here we define the so called sequentially compact acts over semigroups and study some of their categorical and homological properties. Some Baer conditions for injectivity of S-acts are also presented.
[ 3 ] - On Baer type criterion for $C$-dense, $C$-closed and quasi injectivity
For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of monomorphisms in a concrete category $mathcal{C}$, if $mathcal{M}_2subseteq mathcal{M}_1$, then $mathcal{M}_1$-injectivity implies $mathcal{M}_2$-injectivity. The Baer type criterion is about the converse of this fact. In this paper, we apply injectivity to the classes of $C$-dense, $C$-closed monomorphisms. The con...
[ 4 ] - dominating subset and representation graph on topological spaces
Let a topological space. An intersection graph on a topological space , which denoted by , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of and graph properties of are investigated. Also some classifications and representations for the graph ...
[ 5 ] - Categorical properties of regular partially ordered pure monomorphisms
Let a family of monomorphisms in the category A To study mathematical notions in a category A, such as injectivity, tensor products, flatness, with respect to a class M of its (mono)morphisms, one should know some of the categorical properties of the pair (A ,M ). In this paper we take A to be thecategory Pos-S of S-partially ordered sets and to be a particular class o...
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