Domain Semirings United
Uli Fahrenberg, Christian Johansen, Georg Struth, Krzysztof, Ziemi\'anski

TL;DR
This paper explores conditions under which two different axiomatisations of domain operations on semirings are equivalent, unifying previously separate approaches in algebraic structures.
Contribution
It identifies classes of semirings where the two axiomatisations of domain operations coincide, unifying different theoretical frameworks.
Findings
Identifies classes of semirings where the two domain axiomatizations coincide
Provides conditions for the equivalence of the two approaches
Enhances understanding of algebraic structures involving domain operations
Abstract
Domain operations on semirings have been axiomatised in two different ways: by a map from an additively idempotent semiring into a boolean subalgebra of the semiring bounded by the additive and multiplicative unit of the semiring, or by an endofunction on a semiring that induces a distributive lattice bounded by the two units as its image. This note presents classes of semirings where these approaches coincide.
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