Results 31 to 40 of about 104 (51)

On Additivity and Multiplicativity of Centrally Extended (α, β)‐Higher Derivations in Rings

International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.
In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation.
O. H. Ezzat, Attila Gil nyi
wiley   +1 more source

A prime ideal principle for two-sided ideals [PDF]

Communications in Algebra 44 (2016), no. 11, 4585-4608, 2015
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the Prime Ideal Principle for commutative rings due to T.Y. Lam and the author.
arxiv   +1 more source

Every abelian group is the class group of a simple Dedekind domain [PDF]

Trans. Amer. Math. Soc. 369 (2017), no. 4, 2477--2491, 2015
A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, the simple Dedekind domains form a second important class. We show that every abelian group is the class group of a noncommutative simple Dedekind domain.
arxiv   +1 more source

The radical-annihilator monoid of a ring [PDF]

Ryan C. Schwiebert (2016) The radical-annihilator monoid of a ring, Communications in Algebra, 45:4, 1601-1617, 2018
Kuratowski's closure-complement problem gives rise to a monoid generated by the closure and complement operations. Consideration of this monoid yielded an interesting classification of topological spaces, and subsequent decades saw further exploration using other set operations.
arxiv   +1 more source

Prime and semiprime quantum linear space smash products [PDF]

Glasgow Math. J. 63 (2021) 503-514, 2018
Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime.
arxiv   +1 more source

Generalized (m,n)-Jordan centralizers and derivations on semiprime rings [PDF]

arXiv, 2018
In this article, we prove Conjecture $1$ posed in 2013 by Fo$\check{s}$ner \cite{fos} and Conjecture $1$ posed in 2014 by Ali and Fo$\check{s}$ner \cite{ali} related to generalized $(m,n)$-Jordan centralizer and derivation respectively.
arxiv  

An algebraic approach to Wigner's unitary-antiunitary theorem [PDF]

arXiv, 1998
We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wigner-type result for maps on prime C*-algebras.
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 endo-prime and endo-coprime modules [PDF]

arXiv, 2015
The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections are established for endo-prime and endo-coprime modules.
arxiv  

n-Homomorphisms [PDF]

Bull. Iranian Math. Soc. 31 (2005), no. 1, 13-23, 2004
Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}... a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this paper, we investigate $n$-homomorphisms and their relation to homomorphisms.
arxiv