Results 101 to 110 of about 59,526 (169)
Goldie conditions for Ore extensions over semiprime rings [PDF]
arXiv, 2004 Let $R$ be a ring, $\sigma$ an injective endomorphism of $R$ and $\delta$ a $\sigma$-derivation of $R$. We prove that if $R$ is semiprime left Goldie then the same holds for the Ore extension $R[x;\sigma,\delta]$ and both rings have the same left uniform dimension.
arxiv
Structure on the set of closure operations of a commutative ring [PDF]
arXiv, 2008 We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid; however, it is the union of two monoids, one being the left but not right act of the other.
arxiv
On Semiprime Rings with (α,α)-Symmetric Derivations [PDF]
arXiv, 2017 The main purpose of this paper is to study and investigate concerning a ({\alpha},{\alpha})-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a ({\alpha},{\alpha})-symmetric derivations D to satisfy some conditions on R.Where {\alpha}: R to R is an automorphism mapping.
arxiv
Strong commutativity preserving maps on Lie ideals of semiprime rings [PDF]
Beitrage zur algebra und geometrie 49 (2) (2008) 441--447, 2009 Let $R$ be a 2-torsion free semiprime ring and $U$ a nonzero square closed Lie ideal of $R$. In this paper it is shown that if $f$ is either an endomorphism or an antihomomorphism of $R$ such that $f(U)=U,$ then $f$ is strong commutativity preserving on $U$ if and only if $f$ is centralizing on $U.$
arxiv
On generalized Jordan ∗-derivation in rings
Journal of the Egyptian Mathematical Society, 2014 Let n ⩾ 1 be a fixed integer and let R be an (n + 1)!-torsion free ∗-ring with identity element e. If F, d:R → R are two additive mappings satisfying F(xn+1) = F(x)(x∗)n + xd(x)(x∗)n−1 + x2d(x)(x∗)n−2+ ⋯ +xnd(x) for all x ∈ R, then d is a Jordan ...
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Generalized Jordan derivations on semiprime rings [PDF]
arXiv, 2018 The purpose of this note is to prove the following. Suppose $\R$ is a semiprime unity ring having an idempotent element e $\left(e \neq 0, e \neq 1\right)$ which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\R$ is a generalized derivation.
arxiv
Hopfian and Bassian algebras [PDF]
arXiv, 2017 A ring $A$ is called Hopfian if $A$ cannot be isomorphic to a proper homomorphic image $A/J$. $A$ is called Bassian if there cannot be an injection of $A$ into a proper homomorphic image $A/J$. We consider classes of Hopfian and Bassian rings, and tie representability of algebras and chain conditions on ideals to these properties.
arxiv
Primeness, semiprimeness and localisation in Iwasawa algebras [PDF]
arXiv, 2004 Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime, semiprime and a domain. Necessary and sufficient conditions for the localisation at semiprime ideals related to the augmentation ideals of closed normal ...
arxiv
Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images [PDF]
arXivThe class of semiprime left Goldie rings is a huge class of rings that contains many large subclasses of rings -- semiprime left Noetherian rings, semiprime rings with Krull dimension, rings of differential operators on affine algebraic varieties and universal enveloping algebras of finite dimensional Lie algebras to name a few.
arxiv