Abstract
Let A be the variety of associative algebras over a field K and A = K(x1, . . ., xn) be a free associative algebra in the variety A freely generated by a set X = {x1, . . ., xn}, End A the semigroup of endomorphisms of A, and Aut End A the group of automorphisms of the semigroup End A. We prove that the group Aut End A is generated by semi-inner and mirror automorphisms of End A. A similar result is obtained for the automorphism group Aut ao, where ac is the subcategory of finitely generated free algebras of the variety A. The later result solves Problem 3.9 formulated in [17].
| Original language | English |
|---|---|
| Pages (from-to) | 923-939 |
| Number of pages | 17 |
| Journal | International Journal of Algebra and Computation |
| Volume | 17 |
| Issue number | 5-6 |
| DOIs | |
| State | Published - 1 Jan 2007 |
Keywords
- Free algebra
- Semi-inner automorphism
- Variety of associative algebras
ASJC Scopus subject areas
- General Mathematics