On corings and comodules
It is shown that the categories of -coalgebras for a commutative unital ring and the category of -corings for some -algebra as well as their respective categories of comodules are locally presentable.
On countable von Neumann regular rings
On cyclic vertices in valued translation quivers
Let x and y be two vertices lying on an oriented cycle in a connected valued translation quiver (Γ,τ,δ). We prove that, under certain conditions, x and y belong to the same cyclic component of (Γ,τ,δ) if and only if there is an oriented cycle in (Γ,τ,δ) passing through x and y.
On decompositions of d. g. seminear-rings.
On dependent elements in rings.
On derivations and commutativity in prime rings.
On derivations over rings of triangular matrices
On derived equivalence classification of gentle two-cycle algebras
We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
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.