Skolem-Noether algebras

JOURNAL OF ALGEBRA

卷:498

Article

Bresar, Matej^1,2  Hanselka, Christoph³  Klep, Igor³  Volcic, Jurij³ 

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

[3] Univ Auckland, Dept Math, Auckland, New Zealand

关键词: Skolem-Noether theorem;    Automorphism of a tensor product;    Central simple algebra;    Inner automorphism;    Semilocal ring;    Artinian algebra;    Sylvester domain;   

DOI  :  10.1016/j.jalgebra.2017.11.045

来源: Elsevier

【 摘 要 】

An algebra S is called a Skolem-Noether algebra (SN algebra for short) if for every central simple algebra R, every homomorphism R -> R circle times S extends to an inner automorphism of R circle times S. One of the important properties of such an algebra is that each automorphism of a matrix algebra over S is the composition of an inner automorphism with an automorphism of S. The bulk of the paper is devoted to finding properties and examples of SN algebras. The classical Skolem-Noether theorem implies that every central simple algebra is SN. In this article it is shown that actually so is every semilocal, and hence every finite-dimensional algebra. Not every domain is SN, but, for instance, unique factorization domains, polynomial algebras and free algebras are. Further, an algebra S is SN if and only if the power series algebra S[[xi]] is SN. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free