On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
On the numbers of discrete indecomposable modules over tame algebras
On the object-wise tensor product of functors to modules.
On the prime submodules of multiplication modules.
On the Primitivity of Certain Ore Extensions.
On the problem of axiomatization of tame representation type
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the Pythagoras number of orders in totally real number fields.
On the quantum groups and semigroups of maps between noncommutative spaces
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. Sołtan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are...
On the radical theory of involution algebras
On the radical theory of semirings.
On the radicals of near-rings with defect of distributivity.
On the Radicals of Structural Matrix Rings.
On the rank of semimodules over semirings.
On the regularity of group algebras
On the relation between maximal rigid objects and τ-tilting modules
This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in and let Γ be the endomorphism algebra of R. Let F be the functor . We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in via F, and in turn, that projection from to mod Γ sends the maximal rigid objects which have no direct summands from add...
On the Represantation Theory of Artinian Rings and Artins Problems on Division Ring Extensions
On the representation type of one point extensions of tame concealed algebras.
On the representation type of tensor product algebras
The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A ⊗ B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B.
On the representation type of triangular matrix algebras over special algebras