A Note on Generalized Polynomial Identities

Extract

Let A be an algebra with 1 over a field F and let B be a fixed F-basis of A. Let F〈x〉=F〈x₁,…, x_n,…,〉 be the free algebra over F in noncommutative indeterminates x₁,…, x_n,…, and denote by A_F〈x〉 the free product of A and F〈x〉 over F. The elements of A_F〈x〉 of the form varies, repetitions allowed) form an F-basis of A_F〈x〉. They will be referred to as basis monomials, and the involved in a particular basis monomial will be called the coefficients of that basis monomial.