Syntax for Semantics: Krull’s Maximal Ideal Theorem
DOI10.1007/978-3-030-65824-3_6zbMath1490.13001OpenAlexW3196010733MaRDI QIDQ5024726
Daniel Wessel, Peter M. Schuster
Publication date: 27 January 2022
Published in: Paul Lorenzen -- Mathematician and Logician (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-65824-3_6
entailment relationVaihingerAxiom of choicedynamical algebrageometric sequentsdetachable subsetPaul Lorenzenclass inductive definition theoremfinite information topologyFormal Nullstellensatzgeometric entailment relationGilmer radicalKrull's Maximal Ideal Theorem (MIT)Raoult's principle of Open Induction (OI)revised Hilbert Programuseful fictions
History of mathematics in the 20th century (01A60) Biographies, obituaries, personalia, bibliographies (01A70) Philosophical and critical aspects of logic and foundations (03A05) Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Other constructive mathematics (03F65) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Axiom of choice and related propositions (03E25) History of commutative algebra (13-03)
Related Items (6)
Cites Work
- A universal Krull-Lindenbaum theorem
- Space of valuations
- Proving open properties by induction
- Polynomials and radical ideals
- Standard bases for general coefficient rings and a new constructive proof of Hilbert's basis theorem
- A course in constructive algebra
- The origin of Zorn's lemma
- Inductively generated formal topologies.
- Some points in formal topology.
- Krull dimension, Nullstellensätze and dynamical evaluation
- Eliminating disjunctions by disjunction elimination
- Valuative dimension and monomial orders
- Cut elimination for entailment relations
- Lattice-ordered groups generated by an ordered group and regular systems of ideals
- Commutative algebra: constructive methods. Finite projective modules. Translated from the French by Tania K. Roblot
- Constructive commutative algebra. Projective modules over polynomial rings and dynamical Gröbner bases
- Making the use of maximal ideals constructive
- Aspects of general topology in constructive set theory
- Strongly Noetherian rings and constructive ideal theory
- Hilbert rings and the Hilbert Nullstellensatz
- Teilbarkeitstheorie in Bereichen
- Eine Bemerkung über die Abzählbarkeitsvoraussetzung in der Algebra
- Die Erweiterung halbgeordneter Gruppen zu Verbandsgruppen
- Induction in Algebra: a First Case Study
- Induction in Algebra: A First Case Study
- Noetherian orders
- La logique des topos
- A logical approach to abstract algebra
- Finite Methods in Mathematical Practice
- On some peculiar aspects of the constructive theory of point-free spaces
- CONSTRUCTIVE KRULL DIMENSION I: INTEGRAL EXTENSIONS
- The Power of the Ultrafilter Theorem
- What is Noetherian?
- Krull Implies Zorn
- Cut Elimination in the Presence of Axioms
- A New Proof that “Krull implies Zorn”
- Hidden constructions in abstract algebra. Krull Dimension of distributive lattices and commutative rings
- ELIMINATING DISJUNCTIONS BY DISJUNCTION ELIMINATION
- Rings with Primary Ideals as Maximal Ideals.
- A Remark on Rings with Primary Ideals as Maximal Ideals.
- Constructive Aspects of Noetherian Rings
- Proof analysis beyond geometric theories: from rule systems to systems of rules
- Constructing Gröbner bases for Noetherian rings
- Algebraische und logistische Untersuchungen über freie Verbände
- Über halbgeordnete Gruppen
- Dynamical method in algebra: Effective Nullstellensätze
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Syntax for Semantics: Krull’s Maximal Ideal Theorem