Contramodules are module-like algebraic structures endowed with infinite summation (or,
occasionally, integration) operations satisfying natural axioms. Introduced originally by …

For four wide classes of topological rings R, we show that all flat left R-contramodules have
projective covers if and only if all flat left R-contramodules are projective if and only if all left …

Quasi-abelian categories are abundant in functional analysis and representation theory. It is
known that a quasi-abelian category E is a cotilting torsionfree class of an abelian category …

We show that the tensor product of modules of tensor fields is a noetherian module as a
module over any graded Lie subalgebra of finite codimension in the Lie algebra of …

In pursuit of a noncommutative spectrum functor, we argue that the Heyneman-Sweedler
finite dual coalgebra can be viewed as a quantization of the maximal spectrum of a …

The Lie algebra $ gl (V) $ is the Lie algebra of all endomorphisms of a countable-
dimensional complex vector space $ V $. We define a tensor category of topological …

We construct universal monoidal categories of topological tensor supermodules over the Lie
superalgebras gl (V⊕ Π V) and osp (V⊕ Π V) associated with a Tate space V. Here V⊕ Π V …

One-sided exact categories are obtained via a weakening of a Quillen exact category. Such
one-sided exact categories are homologically similar to Quillen exact categories: a one …

We investigate cases where the finite dual coalgebra of a twisted tensor product of two
algebras is a crossed product coalgebra of their respective finite duals. This is achieved by …

We define topologically semiperfect (complete, separated, right linear) topological rings and
characterize them by equivalent conditions. We show that the endomorphism ring of a …