This article is cited in 3 papers

Method of verbal operations and automorphisms of the category of free algebras

E. V. Aladova

Universidade Federal do Rio Grande do Norte, Lagoa Nova

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.

Keywords: variety of algebras, category of free finitely generated algebras, universal algebraic geometry over arbitrary variety of algebras, group of automorphisms, method of verbal operations.

UDC: 512.54.05+512.57

Received: 28.04.2021
Revised: 01.09.2022

DOI: 10.33048/alglog.2022.61.201

 English version: Algebra and Logic, 2022, 61:2, 87–103

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