水平$K$ -代数逆系统的结构
The Structure of the Inverse System of Level $K$-Algebras
摘要：
Macaulay的逆系统是构造具有Gorenstein、水平等性质的Artin K-代数的有效方法，更一般地说，它可以构造具有任意柱脚类型的Artin K-代数。最近，Elias和Rossi给出了任意$d>0$的$d$维Gorenstein K-代数的逆系统的结构.本文通过建立$d$ -维水平K-代数与除幂环的某些子模之间的一一对应，推广了他们的结果。我们给出了几个例子来说明我们的结果。
英文摘要：
Macaulay's inverse system is an effective method to construct Artinian K-algebras with additional properties like, Gorenstein, level, more generally with any socle type. Recently, Elias and Rossi gave the structure of the inverse system of $d$-dimensional Gorenstein K-algebras for any $d>0$. In this paper we extend their result by establishing a one-to-one correspondence between $d$-dimensional level K-algebras and certain submodules of the divided power ring. We give several examples to illustrate our result.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
