Results 1 to 10 of about 60 (25)

A Note On Square-free Commuting Probabilities of Finite Rings [PDF]

, 2023
It is shown that the commuting probability of a finite ring cannot be a fraction with square-free denominator, resolving a conjecture of Buckley and MacHale.
arxiv   +1 more source

Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case [PDF]

, 2011
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.
arxiv   +1 more source

Action of prime ideals on generalized derivations-I [PDF]

arXiv, 2021
In the present paper, we investigate the commutativity of quotient ring $R/P$ where $R$ is any ring and $P$ is a prime ideal of $R$ which admits generalized derivations are satisfying some algebraic identities acting on prime ideals $P$.
arxiv  

Quasi-Duo Skew Polynomial Rings [PDF]

Journal of Pure and Applied Algebra 212 (2008) 1951-1959, 2009
A characterization of right (left) quasi-duo skew polynomial rings of endomorphism type and skew Laurent polynomial rings are given. In particular, it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is commutative modulo its Jacobson radical iff R[x] is left quasi-duo, (2) the skew Laurent polynomial ring is right quasi-duo iff ...
arxiv   +1 more source

Extended Armendariz Rings [PDF]

Algebras Groups Geom., 26(4)(2009), 343-354, 2013
In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their properties.
arxiv  

On Algebraic Multi-Ring Spaces [PDF]

arXiv, 2005
A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with rings in classical ring theory, the conception of multi-ring spaces is introduced. Some characteristics of a multi-ring space are obtained in this paper.
arxiv  

The Avrunin-Scott theorem for quantum complete intersections [PDF]

arXiv, 2008
We prove the Avrunin-Scott theorem for quantum complete intersections; the rank variety of a module is isomorphic to its support variety.
arxiv  

Ext-symmetry over quantum complete intersections [PDF]

arXiv, 2008
We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.
arxiv  

On commuting probabilities in finite groups and rings [PDF]

arXiv, 2020
We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class $\le2$. We believe that these two sets are equal; we prove they are equal, when restricted to groups and rings with odd number of elements.
arxiv  

Some bounds for commuting probability of finite rings [PDF]

arXiv, 2017
Let $R$ be a finite ring. The commuting probability of $R$ is the probability that any two randomly chosen elements of $R$ commute. In this paper, we obtain some bounds for commuting probability of $R$.
arxiv