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On a Class of Automaton Algebras

Part of: Semigroups Theory of computing Chain conditions, growth conditions, and other forms of finiteness Rings with polynomial identity Rings and algebras arising under various constructions

Published online by Cambridge University Press:  19 May 2016

Ferran Cedó  and
Jan Okniński
Ferran Cedó
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain (cedo@mat.uab.cat)
Jan Okniński
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland (okninski@mimuw.edu.pl)
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Abstract

We show that every finitely generated algebra that is a finitely generated module over a finitely generated commutative subalgebra is an automaton algebra in the sense of Ufnarovskii.

Keywords

finitely generated algebraautomaton algebrasemigroupnormal formregular language

MSC classification

Secondary: 16S15: Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) 16S36: Ordinary and skew polynomial rings and semigroup rings 16P40: Noetherian rings and modules 16R20: Semiprime p.i. rings, rings embeddable in matrices over commutative rings 20M05: Free semigroups, generators and relations, word problems 20M25: Semigroup rings, multiplicative semigroups of rings 20M35: Semigroups in automata theory, linguistics, etc. 68Q70: Algebraic theory of languages and automata
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 31 - 38
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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