论文标题
分级交换代数的长度和多重性
Length and Multiplicities in Graded Commutative Algebra
论文作者
论文摘要
本文是对分级交换代数的概念的评论，并特别注意长度和多样性。作者的本文动机来自代数拓扑中的模棱两可的共同体研究，其中模块的分级交换代数与空间的拓扑特性密切相关（如Quillen所示）。本文包括在交换代数社区中以练习或被认为是“民间传说”的结果（及其证明），以及对拓扑相关应用的参考。因此，本文针对的是代数拓扑师和几何图形，以寻求分级的交换代数中的长度和多样性计算的详细说明。
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where the graded commutative algebra of the module is intimately connected to topological properties of the space (as shown by Quillen). Results (and their proofs) which are often left as exercises, or considered 'folklore' in the commutative algebra community are included in this paper, as are references to relevant applications in topology. As such, this paper is aimed at algebraic topologists and geometers looking for a detailed exposition of length and multiplicity computations in graded commutative algebra.
