On the derived category of a finite-dimensional algebra.
On the derived length of units in group algebra
Let be a finite group , a field of characteristic and let be the group of units in . We show that if the derived length of does not exceed , then must be abelian.
On the double Poincaré series of the enveloping algebras of certain graded Lie algebras.
On the Drazin index of regular elements
It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.
On the Embedding of topological domains into quotient fields.
On the endomorphism ring of a semi-injective module.
On the existence of almost split sequences in subcategories
On the existence of projective and quasi-projective covers
On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth
Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
On the family relation for artinian rings
On the Finistic dimension conjecture for Artinian Rings.
On the finiteness of the semigroup of conjugacy classes of left ideals for algebras with radical square zero
Let A be a finite-dimensional algebra over an algebraically closed field with radical square zero, and such that all simple A-modules have dimension at most two. We give a characterization of those A that have finitely many conjugacy classes of left ideals.
On the fragmental structures.
On the Freyd categories of an additive category.
On the Galois structure of algebraic integers and S-units.
On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
On the generalized hypercentralizer of a Lie ideal in a prime ring
On the genus of the graph of tilting modules.
On the Global Dimension of Some Rings.
On the Goeritz Matrix of a Link.