<div class="csl-bib-body">
<div class="csl-entry">Wiesnet, F. (2025, July 14). <i>Constructive Analysis of Maximal Ideals in Z[X] by the Material Interpretation</i> [Conference Presentation]. Computability in Europe 2025, Lissabon, Portugal. http://hdl.handle.net/20.500.12708/223814</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/223814
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dc.description.abstract
We present the concept of material interpretation as a method to transform classical proofs into constructive ones. Using the case study of maximal ideals in Z[X] we demonstrate how a classical implication can be rephrased as a constructive disjunction , with representing a strong form of negation.
The classical proof that every maximal ideal in contains a prime number is revisited, highlighting its reliance on non-constructive principles such as the law of excluded middle. A constructive proof is then developed, replacing abstract constructs with explicit case distinctions and direct computations in Z[X]. This proof clarifies the logical structure and reveals computational content.
We further discusse broader applications, such as Zariski’s Lemma, Hilbert’s Nullstellensatz, and the Universal Krull-Lindenbaum Lemma, with an emphasis on practical implementation using tools such as Python and proof assistants. The material interpretation offers a promising framework for bridging classical and constructive mathematics, enabling algorithmic implementations.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Constructive Algebra
en
dc.subject
Material Interpretation
en
dc.title
Constructive Analysis of Maximal Ideals in Z[X] by the Material Interpretation
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
ESP 576-N
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dc.type.category
Conference Presentation
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tuw.project.title
Materielle Interpretation
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tuw.researchTopic.id
I1
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tuw.researchTopic.name
Logic and Computation
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-02 - Forschungsbereich Computational Logic
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tuw.event.name
Computability in Europe 2025
en
tuw.event.startdate
14-07-2025
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tuw.event.enddate
18-07-2025
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Lissabon
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tuw.event.country
PT
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tuw.event.institution
Association Computability in Europe
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tuw.event.presenter
Wiesnet, Franziskus
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dc.relation.ispreviousversionof
10.1007/978-3-031-95908-0_34
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wb.sciencebranch
Informatik
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1020
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
5
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wb.sciencebranch.value
95
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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item.grantfulltext
none
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item.fulltext
no Fulltext
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crisitem.author.dept
E104-02 - Forschungsbereich Computational Logic
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
