Geodesic
Imbedding of algebras in algebras of triangular matrices
Sbornik. Mathematics, Tome 36 (1980) no. 2, pp. 155-172 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved in the paper that an algebra $R$ which satisfies identities of the form \begin{gather*} [x,y][z,t][x_1,\dots,x_k]=0,\qquad[[x,y],z][x_1,\dots,x_k]=0,\\ [x_1,y_1]\cdot\dotso\cdot[x_l,y_l]=0, \end{gather*} is imbeddable in the algebra $T_n(K)$ of triangular matrices over a commutative algebra $K$. This permits us to answer both the question due to L. Small concerning the imbeddability of an arbitrary nilpotent algebra in a matrix algebra over a commutative algebra and the question of D. Passman on the imbeddability of a group algebra which satisfies a nontrivial identity in a matrix algebra over a commutative algebra. Bibliography: 6 titles. 
@article{SM_1980_36_2_a1,
     author = {A. Z. Anan'in},
     title = {Imbedding of algebras in algebras of triangular matrices},
     journal = {Sbornik. Mathematics},
     pages = {155--172},
     year = {1980},
     volume = {36},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_2_a1/}
}
TY  - JOUR
AU  - A. Z. Anan'in
TI  - Imbedding of algebras in algebras of triangular matrices
JO  - Sbornik. Mathematics
PY  - 1980
SP  - 155
EP  - 172
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1980_36_2_a1/
LA  - en
ID  - SM_1980_36_2_a1
ER  - 
%0 Journal Article
%A A. Z. Anan'in
%T Imbedding of algebras in algebras of triangular matrices
%J Sbornik. Mathematics
%D 1980
%P 155-172
%V 36
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1980_36_2_a1/
%G en
%F SM_1980_36_2_a1
A. Z. Anan'in. Imbedding of algebras in algebras of triangular matrices. Sbornik. Mathematics, Tome 36 (1980) no. 2, pp. 155-172. http://geodesic.mathdoc.fr/item/SM_1980_36_2_a1/

[1] A. I. Maltsev, “O predstavleniyakh beskonechnykh algebr”, Matem. sb., 13(55) (1943), 263–286

[2] A. 3. Ananin, “Lokalno finitno approksimiruemye i lokalno predstavimye mnogoobraziya algebr”, Algebra i logika, 16:1 (1977), 3–23 | MR

[3] J. Lewin, “A matrix representation for associative algebras. I, II”, Trans. Amer. Math. Soc., 188 (1974), 297–317 | MR

[4] I. B. S. Passi, D. S. Passman, S. K. Sehgal, “Lie solvable group rings”, Canad. J. Math., 25:4 (1973), 748–757 | MR | Zbl

[5] D. S. Passman, Infinite group rings, Marcel Dekker inc., New York, 1971 | MR | Zbl

[6] Ring theory (Utah, 1971), Proc. Conf. Ring th., Acad. Press, New York and London, 1972, 381, problem 29 | MR