Results 91 to 100 of about 2,898 (193)
Journal of Algebra, 1978 In this paper we prove that if G is a finite group of automorphisms acting on a semiprime ring R such that R has no additive ] G j-torsion, then the skew group ring R*G is also semiprime. The result was heretofore known in such special cases as when G is finite abelian, R is Goldie, or R satisfies a polynomial identity [I]. Our technique of proof is to
Fisher, Joe W, Montgomery, Susan
openaire +1 more source
Karpatsʹkì Matematičnì Publìkacìï, 2014 We prove that in a ring $R$ with an identity there exists an element $a\in R$ and a nonzero derivation $d\in Der R$ such that $ad(a)\neq 0$. A ring $R$ is said to be a $d$-rigid ring for some derivation $d \in Der R$ if $d(a)=0$ or $ad(a)\neq 0$ for all
O.D. Artemovych, M.P. Lukashenko
doaj +1 more source
Generalized Derivations in Semiprime Gamma Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 LetMbe a 2-torsion-free semiprimeΓ-ring satisfying the conditionaαbβc=aβbαcfor alla,b,c∈M, α,β∈Γ, and letD:M→Mbe an additive mapping such thatD(xαx)=D(x)αx+xαd(x)for allx∈M, α∈Γand for some derivationdofM. We prove thatDis a generalized derivation.
Kalyan Kumar Dey +2 more
openaire +3 more sources
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 +1 more source
GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS [PDF]
Journal of the Australian Mathematical Society, 2019 The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.
Ferreira, Bruno L M +2 more
openaire +2 more sources
On Fully Semiprime Submodules and Fully Semiprime Modules
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017 Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever Xï ...
I.M.A. Hadi, B.N. Shihab
doaj
A Commutativity theorem for semiprime rings [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1980 AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.
openaire +2 more sources
Prime Structures in a Morita Context
, 2018 In this paper, we study on the primeness and semiprimeness of a Morita context related to the rings and modules. Necessary and sufficient conditions are investigated for an ideal of a Morita context to be a prime ideal and a semiprime ideal.
Calci, Mete Burak +3 more
core
Identities with derivations and automorphisms on semiprime rings
International Journal of Mathematics and Mathematical Sciences, 2005 The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative ...
Joso Vukman
doaj +1 more source
A Note on Power Values of Derivation in Prime and Semiprime Rings
Journal of Mathematical Extension, 2012 Let R be a ring with derivation d, such that (d(xy))n = (d(x))n (d(y))n for all x, y ∈ R and n > 1 a fixed integer. In this paper, we show that if R is prime, then d = 0 or R is commutative. If R is semiprime, then d maps R into its center. Moreover
Sh. Sahebi, V. Rahmani
doaj