Hybrid ideals in semigroups

Saima Anis,Madad Khan,Young Bae Jun,Hari M. Srivastava

doi:10.1080/23311835.2017.1352117

Saima Anis, Madad Khan + Show 2 more

Open Access

https://doi.org/10.1080/23311835.2017.1352117

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Abstract

AbstractThe notions of hybrid subsemigroups and hybrid left (resp., right) ideals in semigroups are introduced, and several properties are investigated. Using these notions, characterizations of subsemigroups and left (resp., right) ideals are discussed. The concept of hybrid product is also introduced, and characterizations of hybrid subsemigroups and hybrid left (resp., right) ideals are considered by using the notion of hybrid product. Relations between hybrid intersection and hybrid product are displayed.

Highlights

IntroductionThe study of the fuzzy algebraic structures has started with the introduction of the concepts of fuzzy (subgroupoids) subgroups and fuzzy (left, fight) ideals in the pioneering paper of Rosenfeld (1971)
The study of the fuzzy algebraic structures has started with the introduction of the concepts of fuzzy subgroups and fuzzy ideals in the pioneering paper of Rosenfeld (1971)
We have introduced the concept of hybrid product, and have discussed characterizations of hybrid subsemigroups and hybrid left ideals by using the notion of hybrid product

Summary

Introduction

The study of the fuzzy algebraic structures has started with the introduction of the concepts of fuzzy (subgroupoids) subgroups and fuzzy (left, fight) ideals in the pioneering paper of Rosenfeld (1971). As a parallel circuit of fuzzy sets and soft sets (or, hesitant fuzzy set), Jun, Song, and Muhiuddin (in press) introduced the notion of hybrid structure in a set of parameters over an initial universe set, and applied it to BCK / BCI-algebras and linear spaces. We introduced new kind of ideals in semigroups called as hybrid ideals and have investigated various properties in it Using these notions, we have considered characterizations of subsemigroups and left (right) ideals. We introduce the notions of hybrid subsemigroups and hybrid left (resp., right) ideals in semigroups, and investigate several properties. We introduce the concept of hybrid product, and discuss characterizations of hybrid subsemigroups and hybrid left (resp., right) ideals by using the notion of hybrid product.

Preliminaries

Hybrid subsemigroups and ideals

Conclusion