This article is cited in
5 papers
Imbedding of algebras in algebras of triangular matrices
A. Z. Anan'in
Abstract:
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.
UDC:
519.48
MSC: Primary
16A64; Secondary
16A42,
16A27 Received: 11.11.1977
Fulltext:
PDF file (1467 kB)
