## A matrix representation for associative algebras. I

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- by Jacques Lewin PDF
- Trans. Amer. Math. Soc.
**188**(1974), 293-308 Request permission

## Abstract:

Let*F*be a mixed free algebra on a set

*X*over the field

*K*. Let

*U*,

*V*be two ideals of

*F*, and $\{ \delta (x),(x \in X)\}$ a basis for a free $(F/U,F/V)$-bimodule

*T*. Then the map $x \to (\begin {array}{*{20}{c}} {x + V} & 0 \\ {\delta (x)} & {x + U} \\ \end {array} )$ induces an injective homomorphism $F/UV \to (\begin {array}{*{20}{c}} {F/V} & 0 \\ T & {F/U} \\ \end {array} )$. If $F/U$ and $F/V$ are embeddable in matrices over a commutative algebra, so is $F/UV$. Some special cases are investigated and it is shown that a PI algebra with nilpotent radical satisfies all identities of some full matrix algebra.

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## Additional Information

- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**188**(1974), 293-308 - MSC: Primary 16A64; Secondary 16A42
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338081-5
- MathSciNet review: 0338081