The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...

a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊆ L(X) be a standard operator algebra. Suppose there exists a linear mappi...

A well-known result of Posner’s second theorem states that if the commutator each element in a prime ring and its image under nonzero derivation are central, then is commutative. In present paper, we extended this bluestocking to an arbitrary with involution involving ideals. Further, apart from proving several other interesting exciting results, established ∗-version Vukman’s theorem. Precisel...

In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LAsemigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutr...

Abstract: In this study we introduce a new class of a non-associative algebraic structure namely intra-regular Abel Grassmann's groupoid (AG-groupoid in short). We apply generalized fuzzy ideal theory to this class and discuss its related properties. We introduce ) , ( k q ∨ ∈ ∈ -fuzzy semiprime ideals in AG-groupoids and characterize it. Specifically we have characterized intra-regular AG-grou...

In this paper we have studied   q   , -fuzzy semiprime ideals in semigroups. We have characterized completely regular semigroups by the properties of their   q   , -fuzzy quasi ideals. Moreover we have characterized semigroups that are semilattices of groups by   q   , -fuzzy quasi ideals.

In a recent paper we have extended the classical Herstein's theorem on Jordan derivations on prime rings to Jordan superderivations on prime associative superalgebras. In the present paper we extend this result to semiprime associative superalgebras.

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...