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arXiv · 2409.16192

On semisubtractive ideals of semirings

Amartya Goswami
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Abstract

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.

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Amartya Goswami. 2024-09-24. On semisubtractive ideals of semirings. https://arxiv.org/abs/2409.16192

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