On the symplectic structure of irreducible representation modules of the metacyclic group . (Zur symplektischen Struktur irreduzibler Darstellungsmoduln der metazyklischen Gruppe .)
On the tameness of trivial extension algebras
For a finite dimensional algebra A over an algebraically closed field, let T(A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if is a tilting module and , then T(A) is tame if and only if T(B) is tame.
On the trivial extensions of tubular algebras
The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.
On the unit group of a semisimple group algebra
We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .
On the vertices of modules in the Auslander-Reiten quiver.
On the vertices of modules in the Auslander-Reiten quiver II.
On the Vertices of Modules in the Auslander-Reiten Quiver of p-Groups.
On the weak regularity of semigroup rings.
On the zero set of semi-invariants for quivers
On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
On tilting and cotilting-type modules
We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].
On tilting modules for algebraic groups.
On topologies over rings.
On torsion Gorenstein injective modules
In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if is a Gorenstein integral domain and is a left -module, then the torsion submodule of Gorenstein injective envelope of is also Gorenstein injective. We can also show that if is a torsion -module of a Gorenstein injective integral domain , then the Gorenstein injective envelope of is torsion.
On torsionfree classes which are not precover classes
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite...
On torsion-free periodic rings.
On transitive systems of subspaces in a Hilbert space.
On triangulated orbit categories.
On tubes for blocks of wild type
We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.
On twisted group algebras of OTP representation type
Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and is a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for to be of OTP representation type, in the sense that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and an irreducible -module...