On Simple Ternary 𝚪-Semiring
Journal Title: International Journal of engineering Research and Applications - Year 2017, Vol 7, Issue 2
Abstract
In this paper, the terms, simple ternary Γ-semiring, semi-simple, semisimple ternary Γ-semiring are introduced. It is proved that (1) If T is a left simple ternary Γ-semiringor a lateral simple ternary Γ-semiring or a right simple ternary Γ-semiring then T is a simple ternary Γ-semiring. (2) A ternary Γ-semiring T is simple ternary Γsemiring if and only if TΓTΓaΓTΓT = T for all a T. (3) A ternary Γ-semiring T is regular then every principal ternary Γ-ideal of T is generated by an idempotent. (4) An element a of a ternary Γ-semiring T is said to be semi simple if a n 1 a a i.e. n 1 a a = <a > for all odd natural number n. (5) Let T be a ternary Γ-semiring and a T . If a is regular, then a is semisimple. (17) a be an element of a ternary Γ-semiringT and a is left regular or lateral regular or right regular, then a is semisimple. (18) Let a be an element of a ternary semiring T and if a is intra regular then a is semisimple.
Authors and Affiliations
M. Sajani Lavanya, Dr. D. Madhusudhana Rao, Prof. P. Pnduranga Rao
Keywords
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