Demi-primal algebras
type: Item
instance of: scholarly article
title: Demi-primal algebras
zbMATH Open document ID: 0542.08002
DOI: 10.1007/BF01182253
author: Ágnes Szendrei
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: A finite algebra \({\mathfrak A}=<A,F>\) is called demi-primal if it has no proper subalgebra and every function \(f:A^ n\to A\) admitting the automorphisms of A is a polynomial of A. If \({\mathfrak M}\) is a faithful unitary right R-module, where R is a ring with 1, let \(T({\mathfrak M})\) be the set of operations \(x_ 0r_ 0+...+x_ kr_ k+m,\) with all \(r_ i\in R\), \(m\in M\), and \(r_ 0+...+r_ k=1.\) If q is a prime power, let \(K=GF(q).\) For \(n\geq 1\), let \(K_ n\) be the full \(n\times n\) matrix ring over K. Let \({\mathfrak N}_{n,q}\) be the faithful unitary right module over \(K_ n\), and let \({\mathfrak H}_{n,q}\) be the algebra \(<K^ n;T({\mathfrak N}_{n,q})>\). For prime p, let \({\mathfrak U}_ p\) be the unary algebra on K whose operations are the translations \(x_ 0+a\) (\(a\in A)\). The main result is: A finite algebra with transitive automorphism group is demi- primal if and only if it is simple, it has no proper subalgebra, and it is not equivalent to any of the algebras \({\mathfrak U}_ p\) or \({\mathfrak H}_{n,q}\), where p is prime, \(n\geq 1\), and q is a prime power.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A60
zbMATH DE Number: 3861228
zbMATH Keywords: finite algebra
zbMATH Keywords: faithful unitary right R-module
zbMATH Keywords: transitive automorphism group
reviewed by: Elliott Mendelson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3861228