A Skolem-Noether theorem for coalgebra measurings
type: Item
instance of: scholarly article
title: A Skolem-Noether theorem for coalgebra measurings
zbMATH Open document ID: 0731.16026
DOI: 10.1007/BF01200036
author: M. Koppinen
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: The main theorem of this paper is: Theorem. Let A be a central simple Artinian algebra over a field k, B a finite-dimensional simple subalgebra, and C a k-coalgebra measuring B to A. Assume further that for any simple subcoalgebra D of C, \(B\otimes (D^*)^{op}\) is a simple algebra. Then the measuring is A-inner. This theorem is a true generalization of the classical Skolem-Noether theorem and also implies Jacobson's theorem on inner derivations. The key step in the proof is to show that if A is injective as a (B,A)-bimodule, then if the measuring restricted to the coradical of C is inner, then the measuring is inner.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 4208320
zbMATH Keywords: inner measuring
zbMATH Keywords: central simple Artinian algebra
zbMATH Keywords: finite-dimensional simple subalgebra
zbMATH Keywords: k-coalgebra measuring
zbMATH Keywords: simple subcoalgebra
zbMATH Keywords: Skolem- Noether theorem
zbMATH Keywords: inner derivations
zbMATH Keywords: bimodule
zbMATH Keywords: coradical
reviewed by: Margaret Beattie
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01200036
OpenAlex ID: W1972482276
description: scientific article; zbMATH DE number 4208320