用Betti数和Bass数刻画某些半对偶复形
Characterizing certain semidualizing complexes via their Betti and Bass numbers
摘要：
数值不变量贝蒂数和Bass数是研究交换环上模的大量信息量的有效工具。我们强调这一事实，进一步，通过建立一些标准，某些semidualizing复合物通过他们的贝蒂和巴斯数。半对偶复形的两个主要类型是基础环的移位和对偶复形。设$C$是解析不可约局部环$R$的半对偶复形，且集合$n:=\sup C$和$d:=\dim_RC$ .证明了$C$与$R$的移位拟同构当且仅当$C$的$n$阶贝蒂数为1.证明了$C$是$R$的对偶复形当且仅当$C$的$d$ th Bass数为1.
英文摘要：
It is known that the numerical invariants Betti numbers and Bass numbers are worthwhile tools for decoding a large amount of information about modules over commutative rings. We highlight this fact, further, by establishing some criteria for certain semidualizing complexes via their Betti and Bass numbers. Two distinguished types of semidualizing complexes are the shifts of the underlying rings and dualizing complexes. Let $C$ be a semidualizing complex for an analytically irreducible local ring $R$ and set $n:=\sup C$ and $d:=\dim_RC$. We show that $C$ is quasi-isomorphic to a shift of $R$ if and only if the $n$th Betti number of $C$ is one. Also, we show that $C$ is a dualizing complex for $R$ if and only if the $d$th Bass number of $C$ is one.
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。
