Lattices, spectral spaces, and closure operations on idempotent semirings

DOI10.1016/j.jalgebra.2021.12.007zbMath1491.16046arXiv2001.00808OpenAlexW2997186465MaRDI QIDQ2068141

Jaiung Jun, Jeffrey Tolliver, Samarpita Ray

Publication date: 19 January 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00808

zbMATH Keywords

closure operationcongruencesemiringintegral closurecoherent spacespectral spaceidempotent semiringbounded distributive latticeFrobenius closure\(k\)-idealprime congruencespace of valuationsvaluation order

Mathematics Subject Classification ID

Semirings (16Y60) Ordered topological structures (06F30) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80) Distributive lattices (06D99) Foundations of tropical geometry and relations with algebra (14T10)

Related Items (2)

Vector bundles on tropical schemes ⋮ Proto-exact categories of modules over semirings and hyperrings

Cites Work

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• Boolean Witt vectors and an integral Edrei-Thoma theorem
• An equivalence between two approaches to limits of local fields
• A topological version of Hilbert's Nullstellensatz
• Absolute algebra. III: The saturated spectrum
• Equations of tropical varieties
• The tropical Nullstellensatz for congruences
• Absolute algebra. II: Ideals and spectra
• Supertropical semirings and supervaluations
• Prime and primary ideals in semirings.
• Prime congruences of additively idempotent semirings and a Nullstellensatz for tropical polynomials
• Valuations of semirings
• Projective systemic modules
• Čech cohomology of semiring schemes
• Witt vectors, semirings, and total positivity
• A guide to closure operations in commutative algebra
• Characteristic one, entropy and the absolute point
• A Glimpse at Supertropical Valuation Theory
• Lattice-ordered Rings and Modules
• Tropical ideals
• Closure operations, continuous valuations on monoids and spectral spaces
• Homological algebra in characteristic one
• Spectral Spaces and Ultrafilters
• Prime Ideal Structure in Commutative Rings

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