Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T08:02:34.431Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Class of Automaton Algebras

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

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 ([email protected])
Jan Okniński
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland ([email protected])
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)