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FUNDAMENTAL Γ-SEMIGROUPS THROUGH Hv-Γ-SEMIGROUPS

H. Hedayati, Irina Cristea

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Abstract

In this paper, we consider the notions of Hv- -semigroup and regular relation. Firstly we prove that any semigroup endowed with an equivalence relation can induce an Hv- -semigroup. Secondly, by regular relations, isomorphism theorems on Hv- -semigroups are proved and discussed. Finally, as a strongly regular relation, we point out the fundamental relation on Hv- -semigroups and create a functor between the category of Hv- -semigroups and the category of fundamental -semigroups.

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What this paper is about

In this paper, we consider the notions of Hv- -semigroup and regular relation. Firstly we prove that any semigroup endowed with an equivalence relation can induce an Hv- -semigroup. Secondly, by regular relations, isomorphism theorems on Hv- -semigroups are proved and discussed. Finally, as a strongly regular relation, we point out the fundamental relation on Hv- -semigroups and create a functor between the category of Hv- -semigroups and the category of fundamental -semigroups.

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Available abstract

In this paper, we consider the notions of Hv- -semigroup and regular relation. Firstly we prove that any semigroup endowed with an equivalence relation can induce an Hv- -semigroup. Secondly, by regular relations, isomorphism theorems on Hv- -semigroups are proved and discussed. Finally, as a strongly regular relation, we point out the fundamental relation on Hv- -semigroups and create a functor between the category of Hv- -semigroups and the category of fundamental -semigroups.

Key concepts: Semigroup, Mathematics, Equivalence relation, Special classes of semigroups, Relation (database), Isomorphism (crystallography), Pure mathematics, Bicyclic semigroup

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