We formally introduce and study generalized comatrix coalgebras and upper triangular
comatrix coalgebras, which are not only a dualization but also an extension of classical …

It is well known that the torsion part of any finitely generated module over the formal power
series ring K [[X]] is a direct summand. In fact, K [[X]] is an algebra dual to the divided power …

We study arbitrary algebras all of whose indecomposable finite dimensional representations
are uniserial, or more generally, comodules over serial coalgebras. We show that the infinite …

Given a topological algebra A, we investigate when the categories of all rational A-modules
and of finite-dimensional rational modules are closed under extensions inside the category …

We consider the pure semisimplicity conjecture in the infinite dimensional case: if in the
category A-lf of locally finite left A-modules over an algebra A every object decomposes as a …

We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional
algebras and coalgebras. The key part of the approach is proving new representation …

For coalgebras C over a field, we study when the categories of left C-comodules and of right
C-comodules are symmetric categories, in the sense that there is a duality between the …

In the present text, we examine current trends in the theory of profinite algebras, and
applications, connections and interactions with other fields of mathematics. The thesis …

Let $ C $ be a coalgebra. We investigate the problem of when the rational part of every
finitely generated $ C^* $-module $ M $ is a direct summand $ M $. We show that such a …

We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional
algebras and coalgebras. The key part of the approach is proving new representation …