Results 11 to 20 of about 60 (25)
On generalized commuting probability of finite rings [PDF]
arXiv, 2017 Let $R$ be a finite ring and $r \in R$. The aim of this paper is to study the probability that the commutator of a randomly chosen pair of elements of $R$ equals $r$.
arxiv
The stable AR-quiver of a quantum complete intersection [PDF]
, 2009 We completely describe the tree classes of the components of the stable Auslander-Reiten quiver of a quantum complete intersection. In particular, we show that the tree class is always $A_{\infty}$ whenever the algebra is of wild representation type.
arxiv +1 more source
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
A description of quasi-duo Z-graded rings [PDF]
arXiv, 2009 A description of right (left) quasi-duo Z-graded rings is given. It shows, in particular, that a strongly Z-graded ring is left quasi-duo if and only if it is right quasi-duo. This gives a partial answer to a problem posed by Dugas and Lam in [1].
arxiv
Commuting probabilities of $n$-centralizer finite rings [PDF]
arXiv, 2018 Let $R$ be a finite ring. The commuting probability of $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. $R$ is called an $n$-centralizer ring if it has $n$ distinct centralizers. In this paper, we compute $\Pr(R)$ for some $n$-centralizer finite rings.
arxiv
(Co)homology of quantum complete intersections [PDF]
arXiv, 2007 We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In particular, we show that the cohomology vanishes in high degrees, while the homology is always nonzero.
arxiv
The representation dimension of quantum complete intersections [PDF]
arXiv, 2007 We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the representation dimension of a "homogeneous" quantum complete intersection is strictly larger than its codimension.
arxiv
On splitting polynomials with noncommutative coefficients [PDF]
arXiv, 2007 It is shown that for every splitting of a polynomial with noncommutative coefficients into linear factors $(X-a_{k})$ with $a_{k}$'s commuting with coefficients, any cyclic permutation of linear factors gives the same result and all $a_{k}$ are roots of that polynomial. Examples are given and analyzed from Galois theory point of view.
arxiv
Cohomology of twisted tensor products [PDF]
arXiv, 2008 It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the $\Ext$-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential
arxiv
Centralizing automorphisms and Jordan left derivations on $σ$-prime rings [PDF]
Advances in algebra 1 (1) (2008) 19-26, 2009 Let $R$ be a 2-torsion free $\sigma$-prime ring. It is shown here that if $U\not\subset Z(R)$ is a $\sigma$-Lie ideal of $R$ and $a, b$ in $R$ such that $aUb=\sigma(a)Ub=0,$ then either $a=0$ or $b=0.$ This result is then applied to study the relationship between the structure of $R$ and certain automorphisms on $R$.
arxiv