Geodesic
Almost primitive elements of free nonassociative (anty)commutative algebras of small rank
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 19-24 
A. V. Klimakov. Almost primitive elements of free nonassociative (anty)commutative algebras of small rank. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 19-24. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/
@article{VMUMM_2012_5_a3,
     author = {A. V. Klimakov},
     title = {Almost primitive elements of free nonassociative (anty)commutative algebras of small rank},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {19--24},
     year = {2012},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/}
}
TY  - JOUR
AU  - A. V. Klimakov
TI  - Almost primitive elements of free nonassociative (anty)commutative algebras of small rank
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 19
EP  - 24
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/
LA  - ru
ID  - VMUMM_2012_5_a3
ER  - 
%0 Journal Article
%A A. V. Klimakov
%T Almost primitive elements of free nonassociative (anty)commutative algebras of small rank
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 19-24
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/
%G ru
%F VMUMM_2012_5_a3

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

Criteria for homogeneous elements to be almost primitive are obtained and algorithms to recognize homogeneous almost primitive elements are constructed for free nonassociative commutative and anticommutative algebras of rank $1$ and $2$.

[1] Kurosh A.G., “Neassotsiativnye svobodnye algebry i svobodnye proizvedeniya algebr”, Matem. sb., 20 (1947), 239–262 | MR

[2] Shirshov A.I., “Podalgebry svobodnykh kommutativnykh i antikommutativnykh algebr”, Matem. sb., 34 (1954), 81–88

[3] Mikhalev A.A., Shpilrain V., Yu J.-T., Combinatorial Methods. Free Groups, Polynomials, and Free Algebras, Springer, N.Y., 2004 | MR

[4] Mikhalev A.A., Umirbaev U.U., Yu J.-T., “Automorphic orbits of elements of free non-associative algebras”, J. Algebra, 243 (2001), 198–223 | DOI | MR

[5] Mikhalev A.A., Mikhalev A.V., Chepovskii A.A., Shampaner K., “Primitivnye elementy svobodnykh neassotsiativnykh algebr”, Fund. i prikl. matem., 13:5 (2007), 171–192

[6] Mikhalev A.A., Yu J.-T., “Primitive, almost primitive, test, and $\Delta$-primitive elements of free algebras with the Nielsen–Schreier property”, J. Algebra, 228 (2000), 603–623 | DOI | MR

[7] Klimakov A.V., Mikhalev A.A., “Pochti primitivnye elementy svobodnykh neassotsiativnykh algebr malykh rangov”, Fund. i prikl. matem., 17:1 (2012), 127–141 | MR