On semisubtractive ideals of semirings

A. Goswami

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 T0, 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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(3) (2025), pp. 207-223