The model-theoretic investigation of modules has led to ideas, techniques and results which
are of algebraic interest, irrespective of their model-theoretic significance. It is these aspects …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

Let A be an associative non-positive differential graded ring. In this paper we make a
detailed study of a category Inj (A) of left DG-modules over A which generalizes the category …

We give an account of model theory in the context of compactly generated triangulated and
tensor-triangulated categories ${\cal T} $. We describe pp formulas, pp-types and free …

The relationship between the Ziegler spectrum of (the category of modules over) a ring and
the Ziegler spectrum of its derived category is investigated. Over von Neumann regular rings …

In this paper we introduce and study the so-called continuous $ K $-theory for a certain class
of" large" stable $\infty $-categories, more precisely, for dualizable presentable categories …

Multisorted modules, equivalently representations of quivers, equivalently additive functors
on preadditive categories, encompass a wide variety of additive structures. In addition, every …

Here is yet another “non-commutative geometry”. It can be described briefly as follows: take
a commutative noetherian ring R (eg the coordinate ring of an affine variety); describe Spec …

We give an account of model theory in the context of compactly generated triangulated and
tensor-triangulated categories 𝒯. We describe pp formulas, pp-types and free realisations in …

Multisorted modules, equivalently representations of quivers, equivalently additive functors
on preadditive categories, encompass a wide variety of additive structures. In addition, every …