Article
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A Topology on Sums of Square-Free Ideals in Monoids
Version 1
: Received: 12 May 2024 / Approved: 13 May 2024 / Online: 13 May 2024 (12:30:39 CEST)
How to cite: Matysiak, L. A Topology on Sums of Square-Free Ideals in Monoids. Preprints 2024, 2024050792. https://doi.org/10.20944/preprints202405.0792.v1 Matysiak, L. A Topology on Sums of Square-Free Ideals in Monoids. Preprints 2024, 2024050792. https://doi.org/10.20944/preprints202405.0792.v1
Abstract
In this paper we define families of open sets as sums of idempotent ideals and sums of square-free ideals in a ring. We investigate some topological properties of such topologies. We define the square-free spectrum of a ring as the set of all square-free ideals and examine what topological properties it has for a given monoid.
Keywords
idempotent ideal; monoid; spectrum; square-free ideal; topological space
Subject
Computer Science and Mathematics, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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