Geodesic
A study on ideal elements in ordered $\Gamma$-semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 249-261

Voir la notice de l'article provenant de la source Library of Science

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 $\Gamma$-semirings 
@article{DMGAA_2023_43_2_a6,
     author = {Rao, M. Murali Krishna and Rafi, Noorbhasha and Kumar Kona, Rajendra},
     title = {A study on ideal elements in ordered $\Gamma$-semirings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {249--261},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a6/}
}
TY  - JOUR
AU  - Rao, M. Murali Krishna
AU  - Rafi, Noorbhasha
AU  - Kumar Kona, Rajendra
TI  - A study on ideal elements in ordered $\Gamma$-semirings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2023
SP  - 249
EP  - 261
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a6/
LA  - en
ID  - DMGAA_2023_43_2_a6
ER  - 
%0 Journal Article
%A Rao, M. Murali Krishna
%A Rafi, Noorbhasha
%A Kumar Kona, Rajendra
%T A study on ideal elements in ordered $\Gamma$-semirings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2023
%P 249-261
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a6/
%G en
%F DMGAA_2023_43_2_a6
Rao, M. Murali Krishna; Rafi, Noorbhasha; Kumar Kona, Rajendra. A study on ideal elements in ordered $\Gamma$-semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 249-261. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a6/