Mathematics and Statistics Vol. 12(5), pp. 475 - 483
DOI: 10.13189/ms.2024.120509
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g-inverses in Ternary Semiring

Pandiselvi T. ^*, Anbalagan S.
Department of Mathematics, Rajah Serfoji Govt. College (A), Thanjavur-5, Bharathidasan University, Thiruchirappalli 620 024, Tamil Nadu, India

ABSTRACT

Ternary algebraic systems represent a natural extension of algebraic structures, providing a greater grasp of their features and avenues for further development. Multiplicative semigroups over a field are non-regular, meaning that the regularity equation is not always solvable. When exists, it's referred to as a regular. The regularity requirement is a linear condition that solves linear equations, which makes regular rings significant in many areas of mathematics, particularly in matrix theory. The current state of generalized inverses encompasses many different mathematical fields, including semigroups, operator theory, c^∗-algebras, matrix theory, and semirings. Applications for them can be found in many fields, including robotics, graphics, cryptography, coding theory, Markov chains, linear estimation, differential and difference equations, and graphics. For elements of Ternary semiring, the existence of the generalized inverse is examined. The most general 1- inverse and 1–2 inverse are found for an element over a regular ternary semiring. We looked into the properties and characterization of the g-inverse in ternary Semiring and some fascinating characteristics of the left and right cosets in Partial ordered ternary semiring in this article. Mainly, we investigated the g-inverses using Principal ideals (left and right coset) and found some results in ordered ternary semiring and ternary semiring.

KEYWORDS
Semirings, g-inverses, Ideal, Ordered Ternary Semiring

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Pandiselvi T. , Anbalagan S. , "g-inverses in Ternary Semiring," Mathematics and Statistics, Vol. 12, No. 5, pp. 475 - 483, 2024. DOI: 10.13189/ms.2024.120509.

(b). APA Format:
Pandiselvi T. , Anbalagan S. (2024). g-inverses in Ternary Semiring. Mathematics and Statistics, 12(5), 475 - 483. DOI: 10.13189/ms.2024.120509.