Geodesic
On Some Properties of the Length Function
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 83-91.

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

We study the length of constructions such as a quotient algebra, a direct sum of algebras, and a subalgebra, which occur in the classical Birkhoff theorem. An upper bound for the length of local algebras is obtained.
Keywords: algebra over a field, finitely generated algebra, length function, Birkhoff theorem, direct sum of algebras, Jacobson radical.
Mots-clés : quotient algebra, subalgebra 
@article{MZM_2010_87_1_a8,
     author = {O. V. Markova},
     title = {On {Some} {Properties} of the {Length} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {83--91},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a8/}
}
TY  - JOUR
AU  - O. V. Markova
TI  - On Some Properties of the Length Function
JO  - Matematičeskie zametki
PY  - 2010
SP  - 83
EP  - 91
VL  - 87
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a8/
LA  - ru
ID  - MZM_2010_87_1_a8
ER  - 
%0 Journal Article
%A O. V. Markova
%T On Some Properties of the Length Function
%J Matematičeskie zametki
%D 2010
%P 83-91
%V 87
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a8/
%G ru
%F MZM_2010_87_1_a8
O. V. Markova. On Some Properties of the Length Function. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 83-91. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a8/

[1] R. Pirs, Assotsiativnye algebry, Mir, M., 1986 | MR | Zbl

[2] A. J. M. Spencer, R. S. Rivlin, “The theory of matrix polynomials and its application to the mechanics of isotropic continua”, Arch. Rational Mech. Anal., 2 (1959), 309–336 | DOI | MR | Zbl

[3] A. J. M. Spencer, R. S. Rivlin, “Further results in the theory of matrix polynomials”, Arch. Rational Mech. Anal., 4 (1960), 214–230 | DOI | MR | Zbl

[4] A. Paz, “An application of the Cayley–Hamilton theorem to matrix polynomials in several variables”, Linear and Multilinear Algebra, 15:2 (1984), 161–170 | DOI | MR | Zbl

[5] C. J. Pappacena, “An upper bound for the length of a finite-dimensional algebra”, J. Algebra, 197:2 (1997), 535–545 | DOI | MR | Zbl

[6] G. Birkhoff, “On the structure of abstract algebras”, Math. Proc. Cambridge Philos. Soc., 31 (1935), 433–454 | DOI | Zbl

[7] P. Kon, Universalnaya algebra, Mir, M., 1968 | MR | Zbl

[8] O. V. Markova, “O dline algebry verkhnetreugolnykh matrits”, UMN, 60:5 (2005), 177–178 | MR | Zbl

[9] O. V. Markova, “Vychislenie dlin matrichnykh podalgebr spetsialnogo vida”, Fundament. i prikl. matem., 13:4 (2007), 165–197 | MR

[10] A. E. Guterman, O. V. Markova, “Commutative matrix subalgebras and length function”, Linear Algebra Appl., 430:7 (2009), 1790–1805 | DOI | MR | Zbl