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algebraic independence of elementary symmetric polynomials
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(Theorem)
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Theorem 1 Let $s_1, s_2, \dots, s_n$ be the elementary symmetric polynomials in $n$ variables $t_1, t_2, \dots, t_n$ over a commutative ring $R$ Then $s_1, s_2, \dots, s_n$ are algebraically independent elements of $R[t_1, t_2, \dots, t_n]$ over $R$
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"algebraic independence of elementary symmetric polynomials" is owned by mclase.
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Cross-references: algebraically independent, commutative ring, variables, elementary symmetric polynomials
This is version 2 of algebraic independence of elementary symmetric polynomials, born on 2004-11-16, modified 2004-12-06.
Object id is 6481, canonical name is AlgebraicIndependenceOfElementarySymmetricPolynomials.
Accessed 2609 times total.
Classification:
| AMS MSC: | 05E05 (Combinatorics :: Algebraic combinatorics :: Symmetric functions) |
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Pending Errata and Addenda
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