Results 101 to 110 of about 1,198,003 (194)
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
Multiplicativity of left centralizers forcing additivity
Boletim da Sociedade Paranaense de Matemática, 2014 A multiplicative left centralizer for an associative ring R is a map satisfying T(xy) = T\(x)y for all x,y in R. T is not assumed to be additive. In this paper we deal with the additivity of the multiplicative left centralizers in a ring which contains ...
Mohammad Sayed Tammam El-Sayiad +2 more
doaj +1 more source
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
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
Extracta Mathematicae, 2020 If M is a torsion-free module over an integral domain, then we show that for each submodule N of M the envelope EM (N ) of N in M is an essential extension of N. In particular, if N is divisible then EM (N ) = N .
S.C. Lee, R. Varmazyar
doaj
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
A Some Results on Double Cenralizer for Prime and Semiprime Г- rings
Ibn Al-Haitham Journal for Pure and Applied SciencesThe goal of this work, is to examine the concept of a double centralizer, and double Jordan centralizer on prime and semiprime Г-rings, this is done by studying examples, remarks and results related to that concepts and looking for the ...
Aya Hussein +3 more
doaj +1 more source