On the Finistic dimension conjecture for Artinian Rings.
On the genus of the graph of tilting modules.
On the Global Dimension of Some Rings.
On the lattice of cotilting modules.
One-sided Gorenstein subcategories
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory of an abelian category , and prove that the right Gorenstein subcategory is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When is self-orthogonal, we give a characterization for objects in , and prove that any object in with finite -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in with finite -projective dimension...
Orders of Global Dimension Two.
Predicting syzygies over monomial relations algebras.
QF-3 rings.
Quasi-Hereditary Orders.
Quasitilted algebras have preprojective components
We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
Real representations of quivers
The Dynkin and the extended Dynkin graphs are characterized by representations over the real numbers.
Regularity of the four dimensional Sklyanin algebra
Relative theory in subcategories
We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].
Relative weak derived functors
Let be a ring, a fixed non-negative integer, the class of all left -modules with weak injective dimension at most , and the class of all right -modules with weak flat dimension at most . Using left (right) -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that is right balanced on by , and investigate the global right -dimension of by right derived functors of .
Ringe mit verallgemeinerter Kupischreihe.
Semisimple ring spectra.
Semisimplicity and global dimension of a finite von Neumann algebra
We prove that a finite von Neumann algebra is semisimple if the algebra of affiliated operators of is semisimple. When is not semisimple, we give the upper and lower bounds for the global dimensions of and This last result requires the use of the Continuum Hypothesis.
Some Examples of Orders of Global Dimension Two.
Some remarks on global dimensions for cotorsion pairs
Squared cycles in monomial relations algebras
Let be an algebraically closed field. Consider a finite dimensional monomial relations algebra of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern...