The existence of envelopes
The nilpotency of left noetherian radical rings
The N*-Metric Completion of Regular Rings.
The Rational Invariants of the Tame Quivers.
The relative dihedral homology of involutive algebras.
There is no analog of the transpose map for infinite matrices.
In this note we show that there are no ring anti-isomorphism between row finite matrix rings. As a consequence we show that row finite and column finite matrix rings cannot be either isomorphic or Morita equivalent rings. We also show that antiisomorphisms between endomorphism rings of infinitely generated projective modules may exist.
Tilting Modules of Finite Projective Dimension.
Topologically semiperfect rings
Totally reflexive modules with respect to a semidualizing bimodule
Let and be two associative rings, let be a semidualizing -bimodule. We introduce and investigate properties of the totally reflexive module with respect to and we give a characterization of the class of the totally -reflexive modules over any ring . Moreover, we show that the totally -reflexive module with finite projective dimension is exactly the finitely generated projective right -module. We then study the relations between the class of totally reflexive modules and the Bass class...
Über absolut reine Ringe.
Über kohärente Ringe.
VNR rings, -regular rings and annihilators
Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and -regular rings are studied. Properties of WGP-injectivity are developed.
Weak -injective and weak -fat modules
We introduce and study the concepts of weak -injective and weak -flat modules in terms of super finitely presented modules whose projective dimension is at most , which generalize the -FP-injective and -flat modules. We show that the class of all weak -injective -modules is injectively resolving, whereas that of weak -flat right -modules is projectively resolving and the class of weak -injective (or weak -flat) modules together with its left (or right) orthogonal class forms a hereditary...
When is a quasi-p-projective module discrete?
When is the category of flat modules abelian?
Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.
-чистота модулей над кольцом дискретных нормированний.
Алгебры Хопфа с инволюцией над некоммутативными кольцами и их гомологии. I
Индуктивно замкнутые собственные классы над ограниченными hnp-кольцами.
Индуктивные чистоты в категории модулей
Классификация матричных идемпотентов над подалгеброй K[x], порожденной мономами