Method of Verbal Operations and Automorphisms of the Category of Free Algebras

E. V. Aladova

Research output: Contribution to journalArticlepeer-review

Abstract

Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. This paper is the second in a series of papers started in [Algebra and Logic, 61, No. 1, 1-15 (2022)] where we deal with automorphisms of the category of free finitely generated algebras. Here we describe in detail a method of verbal operations. The method provides a characterization of automorphisms of the category of all free finitely generated algebras in a given variety. The characterization plays a crucial role in universal algebraic geometry. We supply the reader with illuminating examples which clarify the method.

Original languageEnglish
Pages (from-to)87-103
Number of pages17
JournalAlgebra and Logic
Volume61
Issue number2
DOIs
StatePublished - May 2022
Externally publishedYes

Bibliographical note

Funding Information:
E. V. Aladova is supported by the ISF grants 1623/16, 1994/20, and by Gelbart Institute for Mathematical Sciences, Department of Mathematics, Bar-Ilan University, Israel

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

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