Open AccessOn almost nilpotent varieties in theclass of commutative metabelian algebras
Author(s) -
S. P. Mishchenko,
О. В. Шулежко
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-3-21-28
Subject(s) - nilpotent , subvariety , mathematics , variety (cybernetics) , pure mathematics , nilpotent group , locally nilpotent , nilpotent matrix , zero (linguistics) , commutative property , identity (music) , discrete mathematics , algebra over a field , eigenvalues and eigenvectors , physics , linguistics , statistics , state transition matrix , symmetric matrix , philosophy , quantum mechanics , acoustics
A well founded way of researching the linear algebra is the study of it using the identities, consequences of which is the identity of nilpotent. We know the Nagata-Higman’s theorem that says that associative algebra with nil condition of limited index over a eld of zero characteristic is nilpotent. It is well known the result of E.I.Zel’manov about nilpotent algebra with Engel identity. A set of linear algebras where a xed set of identities takes place, following A.I. Maltsev, is called a variety. The variety is called almost nilpotent if it is not nilpotent, but each its own subvariety is nilpotent. Here in the case of the main eld with zero characteristic, we proved that for any positive integer m there exist commutative metabelian almost nilpotent variety of exponent is equal to m.