In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...

Throughout this paper, R will represent an associative ring with center Z(R). A ring R is n-torsion free, where n > 1 is an integer, in case nx = 0, x ∈ R implies x = 0. As usual the commutator xy− yx will be denoted by [x, y]. We will use basic commutator identities [xy,z] = [x,z]y + x[y,z] and [x, yz] = [x, y]z+ y[x,z]. Recall that a ring R is prime if aRb = (0) implies that either a = 0 or b...

In this paper we study certain types of positive fuzzy quasi-orders on semigroups and their links with completely semiprime ideals, prime filters. We characterize various properties a quasi-order Q in terms the its left right eigen spaces IQ CQ, solution sets set equations corresponding to Q. also demonstrate applications obtained results semilattice decompositions semigroups. The shed new ligh...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

The aim of this paper is the study of fuzzy $Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $Gamma$-hyperring under a certain conditions is two-valued.Finally,...

The relations between the radical of crossed product R# σ H and algebra R are obtained. Using this theory, the author shows that if H is a finite-dimensional semisimple, cosemisimle, and either commutative or cocommutative Hopf algebra, then R is H-semiprime iff R is semiprime iff R# σ H is semiprime.

The objective of this paper is to study neutrosophic hypercompositional structures ( ) H I  arising from the hypercompositions derived from the binary relations τ on a neutrosophic set ( ) H I . We give the characterizations of τ that make ( ) H I  hypergroupoids,quasihypergroups, semihypergroups, neutrosophic hypergroupoids, neutrosophic quasihypergroups, neutrosophic semihypergroups and neu...