Homogeneous polynomials | Symmetric functions

Power sum symmetric polynomial

In mathematics, specifically in commutative algebra, the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients can be expressed as a sum and difference of products of power sum symmetric polynomials with rational coefficients. However, not every symmetric polynomial with integral coefficients is generated by integral combinations of products of power-sum polynomials: they are a generating set over the rationals, but not over the integers. (Wikipedia).

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Related pages

Generator (mathematics) | Elementary symmetric polynomial | Commutative algebra | Symmetric polynomial | Characteristic (algebra) | Mathematics | Coefficient | Field (mathematics) | Integer | Complete homogeneous symmetric polynomial | Rational number | Recurrence relation | Polynomial ring | Degree of a polynomial | Ring (mathematics) | Representation theory | Newton's identities | Commutative ring