On group nil rings
On group rings of ordered groups
On group rings with restricted minimum condition.
On Groups and Endomorphism Rings.
On groups of similitudes in associative rings
Let be an associative ring with 1 and the multiplicative group of invertible elements of . In the paper, subgroups of which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.
On groups rings which are not Ore domains.
On -separable and Galois extensions of rings.
On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture
A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.
On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples
It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely...
On Hom-spaces of tame algebras
Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.
On Hopf DeMeyer-Kanzaki Galois extensions.
On Hopf Galois Hirata extensions.
On idempotent elements in certain associative algebras
On idempotent semifields and a paper by H. Hutchins.
On indecomposable projective representations of finite groups over fields of characteristic p > 0
Let G be a finite group, F a field of characteristic p with p||G|, and the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.
On indecomposable representations of quivers with zero-relations
On induced modules over strongly group-graded algebras.
On infinite periodic rings.
On injective -modules.
On injective modules.