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Standard basis in the $T$-ideal formed by polynomial identities of triangular matrices

V. N. Latyshev

M. V. Lomonosov Moscow State University

Abstract: We give the definition of a standard basis of a $T$-ideal of the free associative algebra over a field of zero characteristic and indicate some basis called canonical in the linear space of $n$-linear forms. Using this basis, we construct a standard basis in the $T$-ideal of identities satisfied by the algebra of upper triangular $(n\times n)$-matrices.

UDC: 512.554

 English version: Journal of Mathematical Sciences (New York), 2011, 177:6, 908–914

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