In this study, we prove that let N be a fixed positive integer and R semiprime -ring with extended centroid . Suppose additive maps such is onto, satisfy one of the following conditions belong to Г-N- generalized strong commutativity preserving for short; (Γ-N-GSCP) on Г-N-anti-generalized (Γ-N-AGSCP) Then there exists an element form when condition (i) satisfied, (ii) satisfied

In this paper, we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the reduction theorem for these algebras. We apply to show that are semiprime and completely describe faithfulness arising from systems, in terms dynamics systems. Furthermore, permutative provide a sufficient criteria representation an algebra be equivale...

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...

Let R be a 2-torsion free prime ring with center Z, right Utumi quotient ring U , generalized derivation F associated with a nonzero derivation d of R and L a Lie ideal of R. If F (uv)n = F (u)mF (v)l or F (uv)n = F (v)lF (u)m for all u, v ∈ L, where m,n, l are fixed positive integers, then L ⊆ Z. We also examine the case where R is 312 Ahmad N. Alkenani et al. a semiprime ring. Finally, as an ...

Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K . The anti-automorphism g 7→ g of G can be extended linearly to an anti-automorphism a 7→ a∗ of KG . Let S∗(KG) = {x ∈ U(KG) | x∗ = x} be the set of all symmetric units of U(KG) . We consider the following question: for which groups G and commutative rings K it is true that S∗(KG) is a subgroup in U(KG...

The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let R be a noncommutative prime ring of characteristic different from two and let S and T be left centralizers on R. Suppose that [S(x), T (x)]S(x) + S(x)[S(x), T (x)] = 0 is fulfilled for all x ∈ R. If S 6= 0 (T 6= 0) then there exists λ from the extende...

We investigate antihomomorphic images and pre images of semiprime, strongly primary, irreducible and strongly irreducible fuzzy ideals of a ring. We also prove that: For a surjective anti-homomorphism f : R → R, if every fuzzy ideal of R is f -invariant and has a fuzzy primary (respectively, strongly primary) decomposition in R, then every fuzzy ideal of R has a fuzzy primary (respectively, str...