Fuzzy ideals in $\Gamma-$semiring

TL;DR

This paper explores the relationship between fuzzy ideals in $ ext{Gamma}$-semirings and their operator semirings, establishing lattice equivalences and properties of specific ideal types.

Contribution

It introduces new connections between fuzzy ideals in $ ext{Gamma}$-semirings and operator semirings, including lattice isomorphisms and properties of $k$-ideals and $h$-ideals.

Findings

Lattices of fuzzy left and right ideals are equivalent to those of operator semirings.

Properties relating $k$-ideals and $h$-ideals of $ ext{Gamma}$-semirings with operator semirings are established.

The study provides a framework for understanding fuzzy ideals in $ ext{Gamma}$-semirings through operator semirings.

Abstract

In this paper we have studied the relation between the fuzzy left (respectively right) ideals of $\Gamma-$semiring and that of operator semiring. Thereafter, we have established that the Lattices of all fuzzy left (respectively right) ideal of $\Gamma-$semiring is equivalent to that of Left operator semiring. Also we have established few properties relating the $k-$ideals and $h-$ideals of $\Gamma-$semiring with that of operator semiring.