The double centralizer theorem for semiprime algebras
Journal
Algebras and Representation Theory
Journal Volume
17
Journal Issue
4
Pages
1277-1288
Date Issued
2014
Author(s)
Chuang, C.-L.
Abstract
In the paper we prove the double centralizer theorem for semiprime algebras. To be precise, let R be a closed semiprime algebra over its extended centroid F, and let A be a closed semiprime subalgebra of R, which is a finitely generated module over F. Then C R (A) is also a closed semiprime algebra and C R (C R (A)) = A. In addition, if C R (A) satisfies a polynomial identity, then so does the whole ring R. Here, for a subset T of R, we write CR (T): = {x ∈ R|xt = tx ∀ t ∈ T}, the centralizer of T in R. © 2013 Springer Science+Business Media Dordrecht.
Type
journal article