Irreducible morphisms, the Gabriel-valued quiver and colocalizations for coalgebras.
Moduled categories and adjusted modules over traced rings
CONTENTS1. Introduction.......................................................................................52. Traced rings and adjusted modules..................................................93. Moduled categories.........................................................................214. Triangular adjustments....................................................................325. Categories of matrices and -matrix modules...............436. Trace and cotrace reductions.........................................................477....
On the Represantation Theory of Artinian Rings and Artins Problems on Division Ring Extensions
Representations of bounded stratified posets, coverings and socle projective modules
Stable derived functors of the second symmetric power functor, second exterior power functor and Whitehead gamma functor
On pure global dimension of locally finitely presented Grothendieck categories
On the structure of locally finite pure semisimple Grothendieck categories
Right pure semisimple -hereditary -rings
Tame three-partite subamalgams of tiled orders of polynomial growth
Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders of non-polynomial growth are completely described in Theorem 6.2 and Corollary...
On pure semi-simple Grothendieck categories II
On pure semi-simple Grothendieck categories I
Peak reductions and waist reflection functors
A splitting theorem for multipeak path algebras
Path coalgebras of profinite bound quivers, cotensor coalgebras of bound species and locally nilpotent representations
We prove that the study of the category C-Comod of left comodules over a K-coalgebra C reduces to the study of K-linear representations of a quiver with relations if K is an algebraically closed field, and to the study of K-linear representations of a K-species with relations if K is a perfect field. Given a field K and a quiver Q = (Q₀,Q₁), we show that any subcoalgebra C of the path K-coalgebra K◻Q containing is the path coalgebra of a profinite bound quiver (Q,), and the category C-Comod...
Coalgebras, comodules, pseudocompact algebras and tame comodule type
We develop a technique for the study of K-coalgebras and their representation types by applying a quiver technique and topologically pseudocompact modules over pseudocompact K-algebras in the sense of Gabriel [17], [19]. A definition of tame comodule type and wild comodule type for K-coalgebras over an algebraically closed field K is introduced. Tame and wild coalgebras are studied by means of their finite-dimensional subcoalgebras. A weak version of the tame-wild dichotomy theorem of Drozd [13]...
Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories
Connected sequences of stable derived functors and their applications
CONTENTS1. Introduction........................................................................................................................................................................................................ 52. Category of complexes.................................................................................................................................................................................... 73. Left stable derived functors of covariant functors..........................................................................................................................................
On pure semisimplicity and representation-finite piecewise prime rings
Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem
On the category of commutative connected graded Hopf algebras over a perfect field
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