Results 51 to 60 of about 1,198,003 (194)

On Prime and Semiprime Gamma Rings with Symmetric Gamma n-Centralizers

, 2021
In this paper, we assume that M is Γ-ring then we will present the definition of symmetric Γ-n-centralizers and the definition of Jordan Γ-n-centralizers of M.
Ikram A. Saed
semanticscholar   +1 more source

On τ-centralizers of semiprime rings

Siberian Mathematical Journal, 2007
Let R be a semiprime 2-torsion free ring, and let τ be an endomorphism of R. Under some conditions we prove that a left Jordan τ-centralizer of R is a left τ-centralizer of R. Under the same conditions we also prove that a Jordan τ-centralizer of R is a τ-centralizer of R. We thus generalize Zalar’s results to the case of τ-centralizers of R.
openaire   +4 more sources

On Jordan left-I-centralizers of prime and semiprime gamma rings with involution

Journal of the Egyptian Mathematical Society, 2016
Let M be a 2-torsion free Γ-ring with involution I satisfying the condition xαyβz=xβyαz for all x,y,z∈M and α,β∈Γ. The object of our paper is to show that every Jordan left-I-centralizer on a semiprime Γ-ring with involution I, is a reverse left-I ...
Kalyan Kumar Dey, Akhil Chandra Paul, Bijan Davvaz   +2 more
doaj   +1 more source

On Small Semiprime Modules

, 2021
Let R be a commutative ring with an identity, and G be a unitary R-module. We say that an R-module G is small semiprime if (0 G ) is small Semiprime submodule of G.
H. Ramadhan, N. S. A. Mothafar
semanticscholar   +1 more source

Derivations on semiprime rings [PDF]

Bulletin of the Australian Mathematical Society, 1996
The main result: Let R be a 2-torson free semiprime ring and let D: R → R be a derivation. Suppose that [[D(x), x], x] = 0 holds for all x ∈ R. In this case [D(x), x] = 0 holds for all x ∈ R.
openaire   +2 more sources

Rank of elements of general rings in connection with unit-regularity [PDF]

Journal of Pure and Applied Algebra, 224 (2020), 106211, 2018
We define the rank of elements of general unital rings, discuss its properties and give several examples to support the definition. In semiprime rings we give a characterization of rank in terms of invertible elements. As an application we prove that every element in the socle of a unital semiprime ring is unit-regular.
arxiv   +1 more source

GENERALIZED DERIVATIONS ON SEMIPRIME RINGS [PDF]

Bulletin of the Korean Mathematical Society, 2011
Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, . Then either R is commutative or n = 1, d = 0 and F is the identity map on R.
DE FILIPPIS, Vincenzo, S. Huang
openaire   +2 more sources

THE k-DERIVATION ACTING AS A k-ENDOMORPHISM AND AS AN ANTI-k-ENDOMORPHISM ON SEMIPRIME NOBUSAWA GAMMA RING

, 2014
This article defines k -endomorphism and anti- k -endomorphism on Γ N -rings, and uses the concept of k -derivation of Γ N -rings. Considering M as a semiprime Γ N -ring and d as a k -derivation of M , it aims to prove that (i) if d acts as a k ...
S. Chakraborty, A. C. Paul
semanticscholar   +1 more source

IDENTITIES WITH MULTIPLICATIVE GENERALIZED (α,α)-DERIVATIONS OF SEMIPRIME RINGS

Kragujevac Journal of Mathematics
Let R be a semiprime ring and α be an automorphism of R. A mapping F : R → R (not necessarily additive) is called multiplicative generalized (α,α)-derivation if there exists a unique (α,α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x,
G. Sandhu, A. Ayran, Neşet Aydın
semanticscholar   +1 more source

Derivation alternator rings with S(a, b, c)=0

Boletim da Sociedade Paranaense de Matemática
In this paper, we discuss the derivation alternator rings which are nonassociative but not (-1.1) rings. By assuming some additional conditions, we prove that derivation alternator rings are (-1,1) rings.
P. Sarada Devi, Kommaddi Hari Babu, Y. Suresh Kumar   +2 more
doaj   +1 more source