The number of indecomposable Schur rings over a cyclic 2-group.
The p. p. ring and the Pierce sheaf representation of non-commutative rings
The parametrization of interior algebras.
The primitivity of semigroup algebras of free products.
The radicalness of polynomial rings over nil rings.
The rank of G0 for polycyclic group algebras
The realization of input-output maps using bialgebras.
The representation theory and the branching graph for the family of Turaev algebras .
The resultant of non-commutative polynomials
The Schur Subgroup of a Real Cyclotomic Field.
The special circulant matrix and units in group rings.
The Strong Anick Conjecture is true
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra over a field of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...
The structure of Loewy modules.
The structure of the unit group of the group algebra
The structure of the unit group of the group algebra of the group over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.
The symplectic Gram-Schmidt theorem and fundamental geometries for -modules
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf is appropriately chosen) shows that symplectic -morphisms on free -modules of finite rank, defined on a topological space , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if is an -module (with respect to a -algebra sheaf without zero divisors) equipped with an orthosymmetric -morphism, we show, like in the classical...
The unit group of .
The universal skew field of fractions ofa tensor product of free rings
The upper central series of some matrix groups
Théorème de densité de Tchebotareff et monogénéité de modules sur l'algèbre d'un groupe métacyclique
Thick subcategories of the stable module category
We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...