Symmetric T-ideals (Q1112148)

A T-ideal of a free associative algebra \(k<X>\) is symmetric provided it is closed under the operation of reversing the order of the indeterminates in all the monomials of the polynomial. In this article symmetric T-ideals are studied and a characterization of finitely generated symmetric T-ideals is given. Many examples of symmetric ideals are provided, including the T-ideal of identities and the ideal of weak identities of \(n\times n\) matrices, and also the T-ideal of identities of upper triangular \(n\times n\) matrices.