Domain Semirings United

Uli Fahrenberg; Christian Johansen; Georg Struth; Krzysztof Ziemiański

doi:10.14232/actacyb.291111

Uli Fahrenberg École Polytechnique, France https://orcid.org/0000-0001-9094-7625
Christian Johansen Norwegian University of Science and Technology, Norway https://orcid.org/0000-0002-1525-0307
Georg Struth University of Sheffield, UK https://orcid.org/0000-0001-9466-7815
Krzysztof Ziemiański University of Warsaw, Poland https://orcid.org/0000-0001-7695-4028

DOI: https://doi.org/10.14232/actacyb.291111

Keywords: semirings, quantales, 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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