STANDARD BASIS IN THE T-IDEAL FORMED BY POLYNOMIAL IDENTITIES OF TRIANGULAR MATRICES

摘要

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 × n)-matrices.