Results 41 to 50 of about 201 (72)

SOME RESULTS ON SEMIGROUP IDEALS IN PRIME RING WITH DERIVATIONS

, 2016
Let R be a prime ring, I be a nonzero semigroup ideal of R, d, g, h be derivations of R and a, b ∈ R. It is proved that if d(x) = ag(x)+h(x)b for all x ∈ I and a, b are not in Z(R) then there exists for some λ ∈ C such that h(x) = λ [a, x], g(x) = λ [b ...
A. Ayran
semanticscholar   +1 more source

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

Notes on generalized derivations of *-prime rings

, 2014
Let R be a -prime ring with characteristic different from two and U ¤ 0 be a square closed -Lie ideal of R. An additive mapping F W R! R is called an generalized derivation if there exits a derivation d WR!R such that F.xy/D F.x/yCxd.y/.
E. Koç, N. Rehman
semanticscholar   +1 more source

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

Strong commutativity preserving generalized derivations on triangular rings

, 2014
Let U = Tri(A,M,B) be a triangular ring such that either A or B has no nonzero central ideals. It is shown that every pair of strong commutativity preserving generalized derivations g1,g2 of U (i.e., [g1(x),g2(y)] = [x,y] for all x,y ∈U ) is of the form ...
He Yuan, Yao Wang, Yu Wang, Yiqiu Du
semanticscholar   +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

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  

On Jordan Generalized Higher Reverse Derivations on -rings

, 2014
In this paper, we study the concepts of generalized higher reverse derivation and Jordan generalized higher reverse derivation and Jordan generalized triple higher reverse derivation on -ring M.
S. M. Salih, Marwa Riyadh Salih
semanticscholar   +1 more source

Dual $\pi$-Rickart Modules [PDF]

, 2012
Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S =$ End$_R(M)$. In this paper we introduce dual $\pi$-Rickart modules as a generalization of $\pi$-regular rings as well as that of dual Rickart modules.
Halıcıoglu, Sait, Harmanci, Abdullah, Kurtulmaz, Yosum, Ungor, Burcu   +3 more
core   +1 more source

Derivation which Acts as a Homomorphism or as an Anti-homomorphism in a Prime Ring

, 2007
Let R be a prime ring and S a non-empty subset of R. Suppose that θ, φ are endomorphisms of R. An additive mapping F : R −→ R is called a generalized (θ, φ)-derivation on S if there exists a (θ, φ)derivation d : R −→ R such that F(xy )= F(x)θ(y )+ φ(x)d ...
Asma Ali, Deepak Kumar
semanticscholar   +1 more source