Keith A . Kearnes Quasivarieties of Modules Over Path Algebras of Quivers Dedicated to the memory of Willem Johannes Blok

Relatively Congruence Modular Quasivarieties of Modules

We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows...

Categorical Quasivarieties via Morita Equivalence

We give a new proof of the classification of א0-categorical quasivarieties by using Morita equivalence to reduce to term minimal quasivarieties.

Commutator Theory for Relatively Modular Quasivarieties

We develop a commutator theory for relatively modular quasivarieties that extends the theory for modular varieties. We characterize relatively modular quasivarieties, prove that they have an almost-equational axiomatization and we investigate the lattice of subquasivarieties. We derive the result that every finitely generated, relatively modular quasivariety of semigroups is finitely based.

Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Ideals in Quasivarieties of Algebras