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Unformatted text preview: Theorem 9.6.6. The set of elementary symmetric functions f 1 ;:::; n g in Kx 1 ;:::;x n is algebraically independent over K , and generates K S x 1 ;:::;x n as a ring. Consequently, K. 1 ;:::; n / D K S .x 1 ;:::;x n / . The algebraic independence of the i is the same as linear independence of the monic monomials in the i . First, we establish an indexing system for the monic monomials: A partition is a nite decreasing sequence of nonnegative integers, D . 1 ;:::; k / . We can picture a partition by means of an MbyN matrix of zeroes and ones, where M k...
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 Fall '08
 EVERAGE
 Algebra

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