Abstract
In this research article has to introduce the concept of ternary Γ-semirings.We first consider the congruences and ideals of ternary Γ-semirings then we construct a new ternary Γ-semiring and to be discussed formation of ideals on this ternary Γ-semiring. Also with the help of congruences induced by homomorphism of a ternary Γ-semiring.After that we will establish some of isomorphism theorems and identified the some of commutativity in the diagrams. particularly some fundamental results of ternary Γ-semiring were proved and strengthened.
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