Related papers: Fuzzy ideals in $\Gamma-$semiring
The theory of ternary $\Gamma$-semirings extends classical ring and semiring frameworks by introducing a ternary product controlled by a parameter set $\Gamma$. Building on the foundational axioms recently established by Rao, Rani, and…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…
In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory and lattice theory point of view. Ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic and first, we…
The notion of $\Gamma$-semirings was introduced by Murali Krishna Rao \cite{Rao} as a generalization of the notion of $\Gamma$-rings as well as of semirings. We have known that the notion of $\Gamma$-semirings is a generalization of the…
An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…
The theory of fuzzy semigroups is a branch of mathematics that arose in early 90's as an effort to characterize properties of semigroups by the properties of their fuzzy subsystems which include, fuzzy subsemigroups and their alike, fuzzy…
A subideal is an ideal of an ideal of B(H) and a principal subideal is a principal ideal of an ideal of B(H). We determine necessary and sufficient conditions for a principal subideal to be an ideal of B(H). This generalizes to arbitrary…
This paper shows that the endograph metric and the $\Gamma$-convergence are compatible on a large class of fuzzy set in $\mathbb{R}^m$.
The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
In this paper I reconsider the use of the left ideals of the even-grade subalgebra of spacetime algebra to describe fermionic excitations. When interpreted as rotors the general elements of an even-grade left-ideal describe massless…
In this paper, we have introduced the notion of (1,2)-ideal in an LA-semigroup and shown that (1,2)-ideal and two-sided ideal coincide in an intra-regular LA-semigroup. We have characterized an intra-regular LA-semigroup by using the…
The results on fuzzy ordered semigroups (or on fuzzy semigroups) can be transferred to fuzzy ordered gamma (or to fuzzy gamma) semigroups. We show the way we pass from fuzzy ordered semigroups to fuzzy ordered gamma semigroups.
The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of gamma semigroups in order to…
Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…
In this paper we characterize left(right) ideals, bi-ideals and quasi-ideals of an ordered semigroup by an index $m$ and give some important interplays between these ideals. The concept of m-regularity of an ordered semigroups has been…
In this paper, we have introduced the concept of $\left( \in ,\in \vee q\right) $-fuzzy ideals in a right modular groupoid. We have discussed several important features of a completely regular right modular groupoid by using the $\left( \in…
Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…
This work obtains all the right ideals, radicals, congruences and ideals of the affine near-semirings over Brandt semigroups.
In this paper the notion of quasicoincidence of a fuzzy interval valued with an interval valued fuzzy set, which generalizes the concept of quasicoincidence of a fuzzy point in a fuzzy set is concentrated.