The main purpose of this paper is to investigate some results. When h is ï‡ -(ï¬ ,δ) – Derivation on prime Γ-near-ring G and K is a nonzero semi-group ideal of G, then G is commutative .
In this paper, the structure of and have been introduced and studied. We also obtain that a is of a if and only if there exists an on such that . In addition, we obtain that of if and only if there is an on such that , where are subspaces of with eigenvalues 1 and −1, respectively. We also find t that the existence of on implies that there exists a compatible under appropriate condition.
Let R be an associative ring. In this paper we present the definition of (s,t)- Strongly derivation pair and Jordan (s,t)- strongly derivation pair on a ring R, and study the relation between them. Also, we study prime rings, semiprime rings, and rings that have commutator left nonzero divisior with (s,t)- strongly derivation pair, to obtain a (s,t)- derivation. Where s,t: R®R are two mappings of R.
In the current paper, we study the structure of Jordan ideals of a 3-prime near-ring which satisfies some algebraic identities involving left generalized derivations and right centralizers. The limitations imposed in the hypothesis were justified by examples.
In this paper we show the nilpotency of nilpotent derivation of simeprime Γ-ring with characteristic 2 must be a power of 2 and we show the nilpotency of a nilpotent derivation of simeprime Γ-ring is either odd or a power of 2 without torsion condition.
It is well known that the wreath product is the endmorphism monoid of a free S-act with n-generators. If S is a trivial semigroup then is isomorphic to . The extension for to where is an independent algebra has been investigated. In particular, we consider is to be , where is a free left S-act of n-generators. The eventual goal of this paper is to show that is an endomorphism monoid of a free left S-act of n-generators and to prove that is embedded in the wreath product .
Let M be a weak Nobusawa -ring and γ be a non-zero element of Γ. In this paper, we introduce concept of k-reverse derivation, Jordan k-reverse derivation, generalized k-reverse derivation, and Jordan generalized k-reverse derivation of Γ-ring, and γ-homomorphism, anti-γ-homomorphism of M. Also, we give some commutattivity conditions on γ-prime Γ-ring and γ-semiprime Γ-ring .
The main purpose of this work is to generalize Daif's result by introduceing the concept of Jordan (α β permuting 3-derivation on Lie ideal and generalize these result by introducing the concept of generalized Jordan (α β permuting 3-derivation
This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.