Formularity of sets of Mal'tsev bases, and elementary theories of finite- dimensional algebras. II
type: Item
instance of: scholarly article
title: Formularity of sets of Mal'tsev bases, and elementary theories of finite- dimensional algebras. II
zbMATH Open document ID: 0531.20018
DOI: 10.1007/BF00968739
published in: Siberian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The paper is the second part of an earlier paper of the same authors [see Sib. Mat. Zh. 23, No.5, 152-167 (1982; Zbl 0516.20022)]. After a detailed discussion of a construction of tensor completion of nilpotent groups (a construction analogous to the tensor composition in a module category) new proofs of the classification theorems for k-groups of finite rank are given. In the last paragraph a detailed analysis of the Mal'tsev correspondence and reproved theorems allow to obtain a complete classification of finite-dimensional k-algebras (not necessarily associative and maybe without unit element) with rational structure constants, and if k is regularly separable in terms of their elementary properties.
reviewed by: M.Pałasiński
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20A15
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 3842124
zbMATH Keywords: tensor completion of nilpotent groups
zbMATH Keywords: k-groups
zbMATH Keywords: finite-dimensional k- algebras
author: Alexei Myasnikov
author: Vladimir Remeslennikov
MaRDI profile type: Publication
cites work: Formularity of sets of Mal'tsev bases, and elementary theories of finite algebras. I
cites work: Elementary properties of Abelian groups
full work available at URL: https://doi.org/10.1007/bf00968739
OpenAlex ID: W2085800982
description: scientific article; zbMATH DE number 3842124