DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

M.M.K. Rao

M. Murali Krishna Rao

Department of Mathematics
Sankethika Engineering College
Visakhapatnam-530 041, Andhra Pradesh, India

email: mmarapureddy@gmail.com

R. Kumar Kona

Rajendra Kumar Kona

GITAM(Deemed to be University)

email: rkkona1972@gmail.com

0000-0002-2392-894X

N. Noorbhasha

Rafi Noorbhasha

Department of Mathematics, Bapatla Engineering College
Bapatla-522 101, Andhra Pradesh, India

email: rafimaths@gmail.com

0000-0003-2070-0533

Title:

A study on ideal elements in ordered $Γ$-semirings

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 249-261

Received: 2019-12-31 , Revised: 2022-04-07 , Accepted: 2022-04-07 , Available online: 2023-10-17 , https://doi.org/10.7151/dmgaa.1427

Abstract:

The aim of this paper is to study the structures of some ordered semigroups not only with the ideal elements but also with the generalization of ideal elements. The ideal elements play an important and necessary role in studying the structure of ordered semigroups. We introduce the notion of (ideal, interior ideal, quasi ideal, bi-ideal, quasi interior ideal and weak interior ideal) elements of ordered $Γ$-semirings. We study the properties of ideal elements, relations between them and characterize the ordered $Γ$-semirings, regular ordered $Γ$-semirings and simple ordered $Γ$-semirings using ideal elements. We prove that if $M$ be a simple ordered $Γ$-semiring, then every element of $M$ is an ideal element of $M.$

Keywords:

ideal elements, interior ideal elements, Bi-ideal elements, quasi interior ideal elements, weak interior ideal elements, ordered $Γ$-semirings

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