Some algorithmic questions of associative algebras.
type: Item
instance of: scholarly article
title: Some algorithmic questions of associative algebras.
zbMATH Open document ID: 1044.16019
author: L. Yu. Kasapenko
published in: Russian Mathematics
publication date: 2003-08-11T00:00:00Z
review text: Let \(A=\langle X\mid f_1,\dots,f_m\rangle\) be a finitely presented associative algebra over a field of characteristic 0, where \(\{f_1,\dots,f_m\}\) is a Gröbner (Gröbner-Shirshov) basis. Then \(A\) is called a canonically finitely presented algebra. Let \(B=\langle g_1,\dots,g_N\rangle\) be a subalgebra of \(A\) generated by a SAGBI-basis (Subalgebra Analogue of Gröbner Bases for Ideals) \(\{g_1,\dots,g_N\}\) [\textit{D. Kapur} and \textit{K. Madlener}, Computers and mathematics, Proc. Conf., Cambridge/Mass. 1989, 1-11 (1989; Zbl 0692.13001), \textit{L. Robbiano} and \textit{M. Sweedler}, Lect. Notes Math. 1430, 61-87 (1990; Zbl 0725.13013)]. The following property of \(B\) is algorithmically recognisable: ``\(B\) is a free subalgebra with the free generators \(g_1,\dots,g_N\)''.
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 16-04
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1960517
zbMATH Keywords: Gröbner bases
zbMATH Keywords: SAGBI-bases
zbMATH Keywords: free subalgebras
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1960517