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Spectral Spaces Versus Distributive Lattices: A Dictionary
- Source :
- Advances in Rings, Modules and Factorizations, Advances in Rings, Modules and Factorizations, 321, Springer International Publishing, pp.223-245, 2020, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-030-43416-8_13⟩, Springer Proceedings in Mathematics & Statistics ISBN: 9783030434151
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- The category of distributive lattices is, in classical mathematics, antiequivalent to the category of spectral spaces. We give here some examples and a short dictionary for this antiequivalence. We propose a translation of several abstract theorems (in classical mathematics) into constructive ones, even in the case where points of a spectral space have no clear constructive content.
- Subjects :
- Pure mathematics
Classical mathematics
[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]
010102 general mathematics
Spectral space
Distributive lattice
0102 computer and information sciences
Translation (geometry)
01 natural sciences
Constructive
Distributive property
010201 computation theory & mathematics
Content (measure theory)
Krull dimension
0101 mathematics
ComputingMilieux_MISCELLANEOUS
Mathematics
Subjects
Details
- Language :
- English
- ISBN :
- 978-3-030-43415-1
- ISBNs :
- 9783030434151
- Database :
- OpenAIRE
- Journal :
- Advances in Rings, Modules and Factorizations, Advances in Rings, Modules and Factorizations, 321, Springer International Publishing, pp.223-245, 2020, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-030-43416-8_13⟩, Springer Proceedings in Mathematics & Statistics ISBN: 9783030434151
- Accession number :
- edsair.doi.dedup.....85b60232d209185c138e4f2e1d7ba3cb
- Full Text :
- https://doi.org/10.1007/978-3-030-43416-8_13⟩