Applications of Hyperideals in Characterizations of Left Regular LA-semihyperrings (original) (raw)

On Left Almost Semihyperrings

International Journal of Analysis and Applications, 2018

The purpose of this article is to introduce the notion of left almost semihyperrings which is a generalization of left almost semirings. We investigate the basic properties of left almost semihyperrings. By using the concept of hyperideal and regular relations we prove some useful results on it.

A Study on k-Hyperideals in Ordered Semihyperrings

Symmetry

In this study, we propose the concept of left extension of a hyperideal by generalizing the concept of k-hyperideals in ordered semihyperrings with symmetrical hyper-operation ⊕. By using the notion of extension of a k-hyperideal, we prove some results in ordered semihyperrings. The results of this paper can be viewed as a generalization for k-ideals of semirings.

On the Left and Right Almost Hyperideals of LA-Semihypergroups

International Journal of Fuzzy Logic and Intelligent Systems, 2021

In this paper, we define left almost hyperideals, right almost hyperideals, almost hyperideals, and minimal almost hyperideals. We demonstrate that the intersection of almost hyperideals is not required to be an almost hyperideal, but the union of almost hyperideals is an almost hyperideal, which is completely different from the classical algebraic concept of the ideal theory.

A Note on Left Regular Semiring

In this paper we have focused on the additive and multiplicative identity " e " and determine the additive and multiplicative semigroups. Here we established that, A semiring S in which (S, +) and (S, •) are left singular semigroups, then S is a left regular semiring. We have framed an example for this proposition by considering a two element set.

A Study on the class of Semirings

In this paper, we study the class of Right regular and Multiplicatively subidempotent semirings. Especially we have focused on the additive identity ‘e’ which is also multiplicative identity in both semirings.

A NOVEL APPROACH TOWARDS CLEAN GENERALIZED CHARACTERIZATION OF ORDERED LA-SEMIHYPERGROUP BY RELATIVE HYPERIDEALS

GIS SCIENCE JOURNAL, 9(8)(2022), 370-375. Dr. Abul Basar, Dr. Ayaz Ahmad, Dr Poonam Kumar Sharma and Professor Bhavanari Satyanarayana, 2022, 2022

In this paper, we introduce relative hyperideals, relative quasi-hyperideals, relative bi-hyperideals, relative prime hyperideal, relative semiprime hyperideal, relative quasi-prime hyperideal, relative quasi-semiprime hyperideal, relative quasi-irreducible hyperideal, and relative regularity in ordered LA-semihypergroups. The results in this paper cleanly generalize those in LA-semigroups, LA-Γ-semigroups, ordered LA-semigroups, ordered LA-Γ-semigroups, LA-semihypergroups, LA-Γ-semihypergroups, ordered LA-Γsemihypergroups as well as in ordered LA-semihypergroups by these novel relative hyperideals.

Soft Interior-Hyperideals in Left Regular LA-Semihypergroups

Kragujevac Journal of Mathematics, 2020

This paper is a contribution to the study of the effective content of LAhyperstructure. In this paper, we introduce the notion of soft interior-hyperideals. Further, we give several basic properties of these notions and provide different important characterizations in terms of soft interior hyperideals.

On Minimal and Maximal Hyperidealsin n-ary Semihypergroups

Mathematics

The concept of j-hyperideals, for all positive integers 1≤j≤n and n≥2, in n-ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j-(0-)simple n-ary semihypergroups and discuss their related properties through terms of j-hyperideals. Furthermore, we characterize the minimality and maximality of j-hyperideals in n-ary semihypergroups and establish the relationships between the (0-)minimal, maximal j-hyperideals and the j-(0-)simple n-ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

A NOTE ON RELATIVE TRI QUASI Γ HYPERIDEALS OF Γ SEMIHYPERRING (2024)

ANNALS OF COMMUNICATIONS IN MATHEMATICS, 2024

In this paper, we introduce the concept of tri-quasi hyperideal in Γ-semihyperring generalizing the classical ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal, weak interior ideal, bi-quasi ideal, tri-ideal, quasi-interior ideal and biquasi- interior ideal of Γ-semihyperring and semiring. Furthermore, charecterizations of Γ-semihyperring, regular Γ-semihyperring and simple Γ-semihyperring with relative triquasi hyperideals are provided discussing the characteristics of Γ-semihyperring of relative tri-quasi hyperideals.