On Direct Summands of A-Separable R-Modules.
On discriminants and indices of integers of an algebraic number field.
On domestic algebras of semiregular type
We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.
On -rings
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On embedding of involution rings.
On endomorphism algebras of separable monoidal functors.
On endomorphism algebras over admissible Dedekind domains
On Endomorphism Rings of Primary Abelian Groups.
On Endomorphism Rings of Quasiprojective Modules.
On endomorphisms and quasi-endomorphisms of torsionfree groups
On equivalence of graded rings.
On essential left ideals of associative rings.
On Euclidean Algorithms With Some Particular Properties
On exactness of long sequences of homology semimodules.
On existing of filtered multiplicative bases in group algebras.
On faithful projective representations of finite abelian p-groups over a field of characteristic p
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.
On feebly nil-clean rings
A ring is feebly nil-clean if for any there exist two orthogonal idempotents and a nilpotent such that . Let be a 2-primal feebly nil-clean ring. We prove that every matrix ring over is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.
On filial rings
On Filtered Modules and their Associated Graded Modules.