The theory of idempotent semigroups is of unification type zero
type: Item
instance of: scholarly article
title: The theory of idempotent semigroups is of unification type zero
zbMATH Open document ID: 0626.68070
DOI: 10.1007/BF02328451
author: Franz Baader
published in: Journal of Automated Reasoning
publication date: 1986-01-01T00:00:00Z
review text: An equational theory E is of unification type zero if there exist terms s, t for which there is no minimal complete set of E-unifiers of s, t. The existence of such a theory E was conjectured by Plotkin in 1972. The first example of a theory of this type was constructed by Fage and Huet in 1983. The present paper shows that the theory of idempotent semigroups is of unification type zero. This yields an example of a theory of type zero which is more natural than the example given by Fages and Huet.
Mathematics Subject Classification ID: 68T15
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 4018418
zbMATH Keywords: term rewriting systems
zbMATH Keywords: equational theory
zbMATH Keywords: unification type zero
zbMATH Keywords: theory of idempotent semigroups
MaRDI profile type: Publication
cites work: Q3335752
cites work: Q4126563
cites work: The structure of idempotent semigroups. I
cites work: Idempotent Semigroups
cites work: Q3338215
cites work: A Noetherian and confluent rewrite system for idempotent semigroups
Recommended article: Unification in varieties of idempotent semigroups
Recommended article: A semigroup of theories and its lattice of idempotent elements
Recommended article: Q4384937
Recommended article: Idempotents in semi-convergence semigroups
Recommended article: QUASIVARIETIES OF IDEMPOTENT SEMIGROUPS
Recommended article: Q4018704
Recommended article: The Universal Theory of Ordered Equidecomposability Types Semigroups
Recommended article: Q4232247
Recommended article: Idempotents in \(n\)-ary semigroups
Recommended article: Idempotents in compact monothetic semigroups
description: scientific article; zbMATH DE number 4018418