数学
基数(数据建模)
局部环
诺瑟人
交换性质
同构(结晶学)
戒指(化学)
订单(交换)
组合数学
诺瑟环
同态
交换环
维数(图论)
传递关系
克鲁尔维数
离散数学
纯数学
域代数上的
结晶学
数据挖掘
经济
有机化学
化学
财务
晶体结构
计算机科学
出处
期刊:Mathematica Scandinavica
[Aarhus University Library]
日期:2012-03-01
卷期号:110 (1): 5-5
被引量:8
标识
DOI:10.7146/math.scand.a-15192
摘要
We investigate the set $\mathfrak(R)$ of shift-isomorphism classes of semi-dualizing $R$-complexes, ordered via the reflexivity relation, where $R$ is a commutative noetherian local ring. Specifically, we study the question of whether $\mathfrak(R)$ has cardinality $2^n$ for some $n$. We show that, if there is a chain of length $n$ in $\mathfrak(R)$ and if the reflexivity ordering on $\mathfrak (R)$ is transitive, then $\mathfrak(R)$ has cardinality at least $2^n$, and we explicitly describe some of its order-structure. We also show that, given a local ring homomorphism $\varphi\colon R\to S$ of finite flat dimension, if $R$ and $S$ admit dualizing complexes and if $\varphi$ is not Gorenstein, then the cardinality of $\mathfrak (S)$ is at least twice the cardinality of $\mathfrak (R)$.
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