Automorphisms of categories of free algebras of some varieties

JOURNAL OF ALGEBRA

卷:306

Article

Plotkin, B. ; Zhitomirski, G.

关键词: automorphisms of categories;    inner automorphisms;    free algebras;    associative algebras;    group representations;    universal algebraic geometry;   

DOI  :  10.1016/j.jalgebra.2006.07.028

来源: Elsevier

【 摘 要 】

Let V be a variety of universal algebras. We suggest a method for describing automorphisms of the category of free V-algebras. All automorphisms of such categories are found in two cases: (1) V is the variety of all associative K-algebras over an infinite field K; (2) V is the variety of all representations of groups in unital R-modules over a commutative associative ring R with unit. We prove that all these automorphisms are close to inner automorphisms. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free