On semisubtractive ideals of semirings

Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between \(Q\)-ideals and semisubtractive ideals of semirings, and also study the...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Author: Goswami, Amartya
Format: Article
Language:English
Subjects:
Congruences
Rings (mathematics)
Topology
Online Access:Get full text
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Summary:Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between \(Q\)-ideals and semisubtractive ideals of semirings, and also study them in \(s\)-local semirings. We introduce two subclasses of semisubtractive ideals: \(s\)-strongly irreducible and \(s\)-irreducible, and provide various representation theorems. By endowing a topology on the set of semisubtractive ideals, we prove that the space is \(T_0\), sober, connected, and quasi-compact. We also briefly study continuous maps between semisubtractive spaces. We construct \(s\)-congruences and prove a bijection between these congruences and semisubtractive ideals.
ISSN:2331-8422