A note on the Mac\'ias topology
Jhixon Mac\'ias, Reyes Ortiz
TL;DR
This paper investigates properties of the Macías topology on infinite integral domains, providing topological proofs for algebraic properties and proposing related open problems.
Contribution
It offers new insights into the Macías topology's properties and applies topological methods to algebraic questions in infinite integral domains.
Findings
Topological proofs of maximal ideals' infiniteness
Non-associated irreducible elements are infinite under certain conditions
Analysis of hyperconnectedness in Macías topology
Abstract
In this paper, we study some properties of the closure operator in the Mac\'ias topology on infinite integral domains. Moreover, under certain conditions, we present topological proofs of the infiniteness of maximal ideals and non-associated irreducible elements, taking advantage of the hyperconnectedness of the Mac\'ias topology. Additionally, some problems are proposed.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra