Barycentric algebras and beyond

Adam Komorowski , Anna Romanowska , Jonathan Smith

Abstract

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, (A 15 pkt)
Issue year2019
Vol2019
Pages1-17
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.
DOIDOI:10.1007/s00012-019-0595-3
URL https://link.springer.com/article/10.1007/s00012-019-0595-3
Languageen angielski
Score (nominal)15
ScoreMinisterial score = 15.0, 08-07-2019, 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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