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摘要翻译：
对于任意交换环A，给出了多对称函数环TS^D_a(A[x_1,...,X_r])作为A-代数的显式极小生成元集。在特征零点，即当A是有理数上的代数时，自19世纪以来已知一个最小生成元集。Vaccarino最近也给出了一般情况下的一个相当小的发电机组，但它在一般情况下并不是最小的。给出了生成元的一个尖锐的度界，改进了Fleischmann已有的度界。
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英文标题：
《A minimal set of generators for the ring of multisymmetric functions》
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作者：
David Rydh
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The purpose of this article is to give, for any commutative ring A, an explicit minimal set of generators for the ring of multisymmetric functions TS^d_A(A[x_1,...,x_r]) as an A-algebra. In characteristic zero, i.e. when A is an algebra over the rational numbers, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously obtained by Fleischmann.
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PDF链接：
https://arxiv.org/pdf/0710.0470
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