On the density of fiber sum factors.
On the derived category of a finite-dimensional algebra.
On the endomorphism ring of a semi-injective module.
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 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 Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
On the genus of the graph of tilting modules.
On the homogeneity of additive mappings.
On the Idealizer of a Subring.
On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras
On the lattice of left annihilators of certain rings
On the normal ideals of exchange rings.
On the object-wise tensor product of functors to modules.
On the prime submodules of multiplication modules.
On the Primitivity of Certain Ore Extensions.
On the radicals of near-rings with defect of distributivity.
On the relation between maximal rigid objects and τ-tilting modules
This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in and let Γ be the endomorphism algebra of R. Let F be the functor . We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in via F, and in turn, that projection from to mod Γ sends the maximal rigid objects which have no direct summands from add...