Results 11 to 20 of about 110 (35)

SOME RESULTS ON LIE IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS IN SEMIPRIME RINGS I [PDF]

, 2021
Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R R ! R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U ...
Gölbaşı, Öznur, Koç Sögütcü, Emine   +1 more
core   +1 more source

On McCoy Condition and Semicommutative Rings [PDF]

, 2012
Let $R$ be a ring, $\sigma$ an endomorphism of $R$, $I$ a right ideal in $S=R[x;\sigma]$ and $M_R$ a right $R$-module. We give a generalization of McCoy's Theorem \cite{mccoy}, by showing that, if $r_S(I)$ is $\sigma$-stable or $\sigma$-compatible. Then $
Louzari, Mohamed
core   +3 more sources

On generalized derivations as homomorphisms and anti-homomorphisms [PDF]

, 2004
The concept of derivations as well as generalized derivations (i.e. Ia,b(x) = ax + xb, for all a,b R) have been generalized as an additive function F : R R satisfying F(xy) = F(x)y + xd(y) for all x,y R, where d is a nonzero derivation on R.
Nadeem-úr Rehman
core   +2 more sources

On Commutativity of Rings with Generalized Derivations [PDF]

, 2002
The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a ...
Rehman, Nadeem ur
core   +1 more source

Structure of weakly periodic rings with potent extended commutators [PDF]

, 2001
A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property that, for each x in R, there exists an integer n(x)>1 such that xn(x)=x is necessarily commutative.
Adil Yaqub
core   +2 more sources

Generalized (; )-derivations and Left Ideals in Prime and Semiprime Rings [PDF]

, 2017
Let R be an associative ring, ; be the automorphisms of R, be a nonzero left ideal of R, F : R ! R be a generalized (; )-derivation and d : R ! Rbe an (; )-derivation.
Ali, Asma, Rahaman, Hamidur
core   +2 more sources

Additive Property of Drazin Invertibility of Elements [PDF]

, 2013
In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = \lambda ba$, we show that $a-b$ is Drazin invertible if and only if $aa ...
Chen, Jianlong, Wang, Long, Zhu, Huihui, Zhu, Xia   +3 more
core  

Extended Armendariz Rings [PDF]

, 2013
In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their ...
Agayev, Nazim, Halicioglu, Sait, Harmanci, Abdullah   +2 more
core   +1 more source

On the relation between one-sided duoness and commutators

Open Mathematics
This article studies the structure of rings RR over which the 2×22\times 2 upper triangular matrix rings with the same diagonal are right duo, denoted by D2(R){D}_{2}\left(R).
Kim Nam Kyun, Lee Yang
doaj   +1 more source

On commutativity of σ-prime rings [PDF]

, 2006
Let R be a 2-torsion free σ-prime ring having a σ-square closed Lie ideal U and an automorphism T centralizing on U. We prove that if there exists u0 in Saσ(R) with Ru0 ⊂ U and if T commutes with σ on U, then U is contained in the center of R.
L. Oukhtite, S. Salhi
core   +1 more source