On the regularity of the language of some T-ideals

Lucio Centrone; Alexei Kanel-Belov; Roberto La Scala

doi:10.1016/j.laa.2025.08.002

On the regularity of the language of some T-ideals

Lucio Centrone
, Alexei Kanel-Belov
, Roberto La Scala

Department of Mathematics

University of Bari

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an algebra satisfying a polynomial identity (PI-algebra) and we define what the language generated by its T-ideal is. We conjecture the T-ideal of any PI-algebra is regular and in this paper we give results supporting the conjecture by computing the language of several classes of PI-algebras. Among them, we compute the language generated by some algebras of glued cells that are a useful tool to better understand the so-called Zariski-closed algebras.

Original language	English
Pages (from-to)	61-83
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	727
DOIs	https://doi.org/10.1016/j.laa.2025.08.002
State	Published - 15 Dec 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Keywords

Regular language
Relatively free algebras

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10.1016/j.laa.2025.08.002

Cite this

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KW - Relatively free algebras

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ER -

On the regularity of the language of some T-ideals

Abstract

Bibliographical note

Keywords

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