Barycentric algebras and beyond

Adam Komorowski , Anna Romanowska , Jonathan Smith


Barycentric algebras are fundamental for modeling convex sets, semilattices, affine spaces and related structures. This paper is part of a series examining the concept of a barycentric algebra in detail. In preceding work, threshold barycentric algebras were introduced as part of an analysis of the axiomatization of convexity. In the current paper, the concept of a threshold barycentric algebra is extended to threshold affine spaces. To within equivalence, these algebras comprise barycentric algebras, commutative idempotent entropic magmas, and affine spaces, all defined over a subfield of the field of real numbers. Many properties of threshold barycentric algebras extend to threshold affine spaces.
Author Adam Komorowski (FMIS)
Adam Komorowski,,
- Faculty of Mathematics and Information Science
, Anna Romanowska (FMIS)
Anna Romanowska,,
- Faculty of Mathematics and Information Science
, Jonathan Smith
Jonathan Smith,,
Journal seriesAlgebra Universalis, ISSN 0002-5240, (N/A 70 pkt)
Issue year2019
Publication size in sheets0.8
Keywords in Polishalgebry entropiczne, algebry barycentryczne, zbiory wypukłe, półkraty, samo-dystybutywność, wypukłość
Keywords in Englishentropic algebra, barycentric algebra, convex set, semilattice, self-distributive, convexity
ASJC Classification2602 Algebra and Number Theory
Abstract in PolishW pracy podano konstrukcję progowych algebr anfinicznych. Ponadto zajęto się klasyfikacją reduktów przestrzeni afinicznych.
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 20-10-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.884; WoS Impact Factor: 2017 = 0.608 (2) - 2017=0.553 (5)
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