Dynamic evaluation of integrity and the computational content of Krull's lemma

Schuster, Peter; Wessel, Daniel und Yengui, Ihsen (2021): Dynamic evaluation of integrity and the computational content of Krull's lemma. In: Journal of Pure and Applied Algebra, Vol. 226, No. 1, 106794

Abstract

A multiplicative subset of a commutative ring contains the zero element precisely if the set in question meets every prime ideal. While this form of Krull's Lemma takes recourse to transfinite reasoning, it has recently allowed for a crucial reduction to the integral case in Kemper and the third author's novel characterization of the valuative dimension. We present a dynamical solution by which transfinite reasoning can be avoided, and illustrate this constructive method with concrete examples. We further give a combinatorial explanation by relating the Zariski lattice to a certain inductively generated class of finite binary trees. In particular, we make explicit the computational content of Krull's Lemma. (c) 2021 Elsevier B.V. All rights reserved.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0022-4049
• Language: English