Automorphisms and derivations of commutative and PI-algebras (Q6551460)

The article under review is an abridged version of the authors' publication ``Automorphisms and derivations of affine commutative and PI-algebras'' [Trans. Am. Math. Soc. 377, No. 2, 1335--1356 (2024; Zbl 1547.13036)]. In this abridgment, the authors provide a concise discussion of the main theorems presented in [loc. cit.]. The achieved results extend the classical theorem of A. Selberg's for finitely generated subgroups of Aut(\(A\)) and of Engel's theorem for subalgebras of Der(\(A\)) for a finitely generated associative commutative algebra \(A\) over an associative commutative ring. For a detailed review the reader may look at [loc. cit.].\N\NFor the entire collection see [Zbl 1539.11006].