Homogeneously simple associative algebras.
type: Item
instance of: scholarly article
title: Homogeneously simple associative algebras.
zbMATH Open document ID: 1236.16038
DOI: 10.3103/S1066369X11050033
published in: Russian Mathematics
publication date: 2011-11-21T00:00:00Z
review text: Suppose that \(G\) is group and \(A=\bigoplus_{g\in G}A_g\) is a \(G\)-graded algebra over a field \(k\). It is assumed that in \(A\) for any elements \(a_i\in A_{g_i}\), \(i=1,2,3,\) there exists a non-zero element \(\lambda(g_1,g_2,g_3)\in k\) such that \((a_1a_2)a_3=\lambda(g_1,g_2,g_3)a_1(a_2a_3)\). Suppose that the field \(k\) is algebraically closed and \(A\) has no nontrivial homogeneous ideals. Then \(A=B\text{Mat}(n,k)\), where \(B\) is a homogeneous field and \(\text{Mat}(n,k)\) is a full matrix algebra of size \(n\) over \(k\).
reviewed by: Vyacheslav A. Artamonov
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 17A60
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 5975538
zbMATH Keywords: graded algebras
zbMATH Keywords: homogeneously simple algebras
author: Nikolai A. Koreshkov
MaRDI profile type: Publication
cites work: Finite-dimensional homogeneously simple algebras of associative type
cites work: Identities of graded algebras
cites work: A class of algebras of associative type
cites work: Modules and ideals of algebras of associative type
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description: scientific article; zbMATH DE number 5975538