Work

On the finite generation of ideals in tensor triangular geometry

Year: 2026

Type: article

Abstract: Inspired by Cohen's characterization of Noetherian commutative rings, we study the finite generation of ideals in tensor triangular geometry. In particular, for an essentially small tensor triangulated category with weakly Noetherian spectrum, we show that every prime ideal in can be generated by finitely many objects if and only if the set of prime ideals of is finite.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70355

Author: Tobias Barthel

Institution: Max Planck Institute for Mathematics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Engineering and Physical Sciences Research Council, European Research Council, HORIZON EUROPE European Research Council