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Ternary Hemirings and ternary Semirings: Definitions and examples

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Author: 
Gudikandula. Srinivasa Rao, Madhusudhana Rao, D. and Srinivasa Rao, G.
Abstract: 

In this paper we mainly introduce the some special notions of ternary semi rings and we gave examples of definitions and we prove that a set T containing two distinct elements 0 and 1 and on which operations + and [ ] are defined is a commutative ternary semi ring if and only if the following conditions are satisfied for all a, b, c, d, e, f ∈ T: (1) a + 0 = 0 + a = a; (2) a11 = a; (3) 00a =0; (4) [(aeg+ b)+ c]df = dfb+ [ae(gdf) + cdf].

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