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Finitely and non-finitely related words.

Authors :
Glasson, Daniel
Source :
Semigroup Forum. Oct2024, Vol. 109 Issue 2, p347-374. 28p.
Publication Year :
2024

Abstract

An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many interesting properties with respect to the finite basis problem. We show that much of this intriguing behaviour extends to the world of finite relatedness by using interlocking patterns called chain, crown, and maelstrom words. In particular, we show that there are large classes of non-finitely related nilpotent monoids that can be used to construct examples of: ascending chains of varieties alternating between finitely and non-finitely related; non-finitely related semigroups whose direct product are finitely related; the addition of an identity element to a non-finitely related semigroup to produce a finitely related semigroup. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
*ALGEBRA
*VOCABULARY
*MONOIDS

Details

Language :
English
ISSN :
00371912
Volume :
109
Issue :
2
Database :
Academic Search Index
Journal :
Semigroup Forum
Publication Type :
Academic Journal
Accession number :
179815144
Full Text :
https://doi.org/10.1007/s00233-024-10452-8