On the homomorphisms of $\cap$-structure spaces

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematical Science and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

10.48308/cgasa.2024.235060.1476

Abstract

 In \cite{cap}, the concept of $\cap$-structure space is defined and it is studied from an algebraic and topological points of view. Indeed, the $\cap$-structure  is considered as a model for all algebraic substructures such as subgroups, subrings and submodules, ideals, etc. Moreover, the elements of these $\cap$-structures are seen as an open set, and from this point of view, another goal is to relate some  algebraic properties to some topological properties. The present article follows the same points of view of \cite{cap}. In particular, similar to algebraic homomorphisms, $\cap$-structural homomorphisms  are defined and investigated in $\cap$-structure spaces. In addition, we examine some classical results related to homomorphisms. In this regard, similar to lattice theory, we define the congruence relation on $\cap$-structure spaces and give some facts about them, and then we generalize the isomorphism theorems of algebraic structure to $\cap$-structure spaces.   

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 17 November 2024

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