Group graded rings and smash products
type: Item
instance of: scholarly article
title: Group graded rings and smash products
zbMATH Open document ID: 0602.16002
author: Constantin Năstăsescu
author: Nicola Rodinò
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
review text: Let \(G\) be a finite group with identity element \(e\). Let \(R\) be a \(G\)-graded algebra over a commutative ring \(k\). As in a paper by \textit{M. Cohen} and \textit{S. Montgomery} [Trans. Am. Math. Soc. 282, 237--258 (1984; Zbl 0533.16001)], one forms the smash product \(R\#(kG)^*\) (where \((kG)^*\) is the dual of the group ring \(kG)\), and deduces from certain duality theorems, various connections between \(R\), \(R_e\) and \(R\#(kG)^*\). In this paper the authors characterize \(R\#(kG)^*\) via endomorphism rings of an \(R\)-generator. They deduce from it a slight generalization of the duality theorems proved by Cohen and Montgomery.
reviewed by: Miriam Cohen
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 3970958
zbMATH Keywords: G-graded algebra
zbMATH Keywords: smash product
zbMATH Keywords: dual of the group ring
zbMATH Keywords: duality theorems
zbMATH Keywords: endomorphism rings
MaRDI profile type: Publication
cites work: Group-Graded Rings, Smash Products, and Group Actions
cites work: Q3957087
cites work: Q4049223
description: scientific article; zbMATH DE number 3970958