Let / and g be functions of a set 5 into a semiprime ring R. A necessary and sufficient condition for / and g to satisfy f{s)xg{t) = g{s)xf{t) for all s, t e S, x e R is given. As an application, biderivations and commuting additive mappings of semiprime rings are characterized.

We first provide an example of a ring R such that all possible 2 × 2 structural matrix rings over R are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix B of a structural matrix ring M(B,R) over a semiprime Noetherian ring R can be recovered, contrary to the ...

The purpose of this paper is to study some properties of cartesian product of fuzzy completely prime ideals and fuzzy completely semiprime ideals of Γ-semigroups. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between cartesian product of fuzzy ideals (fuzzy completely prime ideals, fuzzy completely semiprime ideals) of a Γ-semigroup and that of it...

In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) ...

Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly rings and invertible discuss the relations between these several properties of rings. Also, study concept crossed products some defined product give relationship Moreover, in generalization for essential submodules, semi-uniform modules which is uniform modules.

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

Fermionic-type character formulae are presented for charged irreducible modules of the graded parafermionic conformal field theory associated to the coset ôsp(1, 2)k/û(1). This is obtained by counting the weakly ordered ‘partitions’ subject to the graded Z̃k exclusion principle. The bosonic form of the characters is also presented.

In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...