Formularity of sets of Mal'tsev bases, and elementary theories of finite- dimensional algebras. II
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.
scientific article; zbMATH DE number 3842124