From subtractive ideals of semirings to deductive and inductive sets in general algebras

TL;DR

This paper generalizes the concept of subtractive ideals from semirings to broader algebraic structures, analyzing their counterparts and properties across various algebraic contexts.

Contribution

It extends the characterization of kernels as subtractive ideals to general algebras and explores their analogs in different algebraic frameworks.

Findings

Characterization of kernels as subtractive ideals in general algebras

Analysis of subtractive and ideal counterparts in multiple algebraic settings

Extension of algebraic ideal concepts beyond semirings

Abstract

In this paper we extend the characterisation of kernels in semirings as subtractive ideals to general algebras. We then analyse the counterparts of ``subtractive'' and ``ideal'' in several different algebraic settings.