Topologische und algebraische Filter
Holger Brenner
TL;DR
This paper characterizes the set of filters in a topologically structured commutative monoid, exploring the properties of the spaces formed by these filters, akin to spectral spaces in algebraic geometry.
Contribution
It introduces a framework for analyzing filters in topological monoids and studies the topological spaces they generate, extending classical algebraic concepts.
Findings
Identification of the set of filters as saturated submonoids
Analysis of the topological properties of the filter spaces
Connection to spectral spaces in algebraic geometry
Abstract
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
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Taxonomy
TopicsRings, Modules, and Algebras · Polynomial and algebraic computation · Commutative Algebra and Its Applications