are useful in abstract algebra for generating mathematical structures. For example, given a field , the set of polynomials with coefficients in is the polynomial ring with polynomial addition and multiplication as operations. In particular, if two indeterminates and are used, then the polynomial ring also uses these operations, and convention holds that . Indeterminates may also be used to generate a free algebra over a commutative ring . For instance, with two indeterminates and , the free algebra includes sums of strings in and , with coefficients in , and with the understanding that and are not necessarily identical (since free algebra is by definition non-commutative). See also Indeterminate equation Indeterminate form Indeterminate system Polynomial Formal power series Notes References Abstract algebra Polynomials Mathematical series