Geodesic
On a~Shirshov basis of relatively free algebras of complexity~$n$
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 363-374

Voir la notice de l'article provenant de la source Math-Net.Ru

A Shirshov basis is a set of elements of an algebra $A$ over which $A$ has bounded height in the sense of Shirshov. A description is given of Shirshov bases consisting of words for associative or alternative relatively free algebras over an arbitrary commutative associative ring $\Phi$ with unity. It is proved that the set of monomials of degree at most $m^2$ is a Shirshov basis in a Jordan PI-algebra of degree $m$. It is shown that under certain conditions on $\operatorname{var}(B)$ (satisfied by alternative and Jordan PI-algebras), if each factor of $B$ with nilpotent projections of all elements of $M$ is nilpotent, then $M$ is a Shirshov basis of $B$ if $M$ generates $B$ as an algebra. Bibliography: 12 titles. 
@article{SM_1989_63_2_a6,
     author = {A. Ya. Belov},
     title = {On {a~Shirshov} basis of relatively free algebras of complexity~$n$},
     journal = {Sbornik. Mathematics},
     pages = {363--374},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a6/}
}
TY  - JOUR
AU  - A. Ya. Belov
TI  - On a~Shirshov basis of relatively free algebras of complexity~$n$
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 363
EP  - 374
VL  - 63
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a6/
LA  - en
ID  - SM_1989_63_2_a6
ER  - 
%0 Journal Article
%A A. Ya. Belov
%T On a~Shirshov basis of relatively free algebras of complexity~$n$
%J Sbornik. Mathematics
%D 1989
%P 363-374
%V 63
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1989_63_2_a6/
%G en
%F SM_1989_63_2_a6
A. Ya. Belov. On a~Shirshov basis of relatively free algebras of complexity~$n$. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 363-374. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a6/