Results 41 to 50 of about 205 (70)

ON CERTAIN DIFFERENTIAL IDENTITIES IN PRIME RINGS WITH INVOLUTION

, 2015
In the present paper we investigate commutativity of -prime ring R, which satisfies certain differential identities on -ideals of R. Some results already known for prime rings on ideals have also been deduced.
M. Ashraf, M. Siddeeque
semanticscholar   +1 more source

On rings with prime centers

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 667-670, 1994., 1993
Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non‐commutative ring with a prime center is given.
Hazar Abu-Khuzam, Adil Yaqub
wiley   +1 more source

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

A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi, Hafedh Alnoghashi, Radwan Mohammed Al-Omary, Abdelkarim Boua, Faranak Farshadifar   +4 more
wiley   +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  

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

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

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

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