Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...

Let R be a prime ring of characteristic different from 2, with extended centroid C, U its two-sided Utumi quotient ring, F a nonzero generalized derivation of R, f(x 1,…, x n ) a noncentral multilinear polynomial over C in n noncommuting variables, and a, b ∈ R such that a[F(f(r 1,…, r n )), f(r 1,…, r n )]b = 0 for any r 1,…, r n ∈ R. Then one of the following holds: (1) a = 0; (2) b = 0; (3) ...

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

The algorithms for linear algebra in the Magma and Axiom computer algebra systems work over an arbitrary ring. For example, the implementation of Gaussian elimination for reducing a matrix to (reduced) row Echelon form works over any field that the user constructs. In contrast, Maple’s facilities for linear algebra in its LinearAlgebra package only work for specific rings. If the input matrix c...

In this paper we look at two categories, the category F of fuzzy subsets and a quotient category F=M of fuzzy sets. The category F=M is an extension of the category of sets, and the standard constructions in fuzzy set theory arise naturally within this category.

This paper aims to introduce fuzzy congruence relations over Heyting algebras (HA) and give constructions of quotient Heyting algebras induced by fuzzy congruence relations on HA. The Fuzzy First, Second and Third Isomorphism Theorems of HA are established. MSC: 06D20, 06D72, 06D75.

Recommended by Akbar Rhemtulla We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

In this paper we introduce and analyze the notion of fuzzy hyperideal of a fuzzy hyperring. Then we investigate some properties based on homomorphisms between fuzzy hyperrings. Also, we try to extend the notion of cuts in fuzzy structures for fuzzy hyperrings. We study the quotient structure of a fuzzy hyperring and also we define fuzzy hypercongruences. Then we investigate some connections bet...