Local \varepsilon _0-characters in torsion rings

Characterization of $(delta‎, ‎varepsilon)$-double derivation on rings ‎and ‎algebras

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

On torsion-free periodic rings

There is a great deal of literature on periodic rings, respectively, torsion-free rings (especially of rank two). The aim of this paper is to provide a link between these two topics. All groups considered here are Abelian, with addition as the group operation. By order of an element we always mean the additive order of this element. All rings are associative but not necessarily with identity. T...

Flatness and Torsion in Tensor Powers of Modules over Local Rings

This is a fairly literal transcript of my lectures at the 7th Japan-Vietnam Joint Seminar on Commutative Algebra, held in Quy Nhon, Vietnam, from 12th–16th December 2011. The aim of those lectures was to describe my recent work with Avramov [2] on a conjecture of Vasconcelos [18] concerning the relationship between flatness and torsion in tensor product of modules over regular rings, that in tu...

2-Groups, 2-Characters, and Burnside Rings

We study 2-representations, i.e. actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno formula for the Ganter-Kapranov 2-charact...

On Torsion Subgroups in Integral Group Rings of Finite Groups