This book provides the first extensive and systematic treatment of the theory of commutative
coherent rings. It blends, and provides a link, between the two sometimes disjoint …

We construct a natural continuous map from the triangular spectrum of a tensor triangulated
category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

The concept of an abelian DG-category, introduced by the first-named author in Positselski
(Exact DG-categories and fully faithful triangulated inclusion functors. arXiv: 2110.08237 …

Cet article passe en revue les principaux resultats connus au sujet des anneaux et modules
coherents, et resoud un certain nombre de probltmes a l'aide d'une nouvelle notion …

The aim of this note is to understand under which conditions invertible modules over a
commutative-algebra in the sense of Elmendorf, Kriz, Mandell & May give rise to elements in …

Let X be a smooth p-adic formal scheme. We show that integral crystalline local systems on
the generic fiber of X are equivalent to prismatic F-crystals over the analytic locus of the …

S-domains and strong S-rings are studied extensively with special emphasis on integral and
polynomial ring extensions. The main theorem of this paper is that for a Prüfer domain R, the …

The theory of algebras, rings, and modules is one of the fundamental domains of modern
mathematics. General algebra, more specifically non-commutative algebra, is poised for …

We study two notions of purity in categories of sheaves: the categorical and the geometric. It
is shown that pure injective envelopes exist in both cases under very general assumptions …