Abstract
Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. In universal algebraic geometry over an arbitrary variety of algebras, the group of automorphisms of the category of free finitely generated algebras plays an important role. This paper is first in a series where we will deal with the group mentioned. Here we describe properties of automorphisms of the category of all free finitely generated algebras and distinguish two important subgroups: namely, the subgroup of inner automorphisms and the subgroup of strongly stable automorphisms.
| Original language | English |
|---|---|
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Algebra and Logic |
| Volume | 61 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Funding
Supported by the ISF grants 1623/16, 1994/20, and by Gelbart Institute for Mathematical Sciences, Department of Mathematics, Bar-Ilan University, Israel.
| Funders | Funder number |
|---|---|
| Gelbart Institute for Mathematical Sciences | |
| Department of Mathematics, Bar-Ilan University | |
| Israel Science Foundation | 1623/16, 1994/20 |
Keywords
- category of free finitely generated algebras
- group of automorphisms
- universal algebraic geometry over arbitrary variety of algebras
- variety of algebras