TL;DR
This paper proves that the set of proper ideals of a monoid, when equipped with a specific topology, forms a spectral space, linking algebraic structures with topological properties.
Contribution
It introduces a novel topological perspective on monoid ideals by demonstrating their spectral space structure under coarse lower topology.
Findings
Proper ideals of monoids form spectral spaces with coarse lower topology
Establishes a connection between algebraic and topological properties of monoids
Provides a new framework for analyzing monoid ideals
Abstract
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Rings, Modules, and Algebras