Iwasawa代数中的自反理想
Reflexive Ideals in Iwasawa Algebras
摘要：
设$G$是无挠紧$p$ -adic解析群.给出了$p$和$G$的充分条件，保证了$G$的Iwasawa代数$Ω_G$没有非平凡的双边自反理想.因此，这些条件意味着$Ω_G$中的每个非零正规元素都是一个单位。我们证明了当$G$是$\SL_2(\Zp)$的开子群且$p$是任意的时，这些条件成立.利用第一作者的一个结果，证明了当$G$是$\SL_2(\Zp)$的同余子群时，$Ω_G$中只有两个素理想：零理想和唯一的极大理想.这些陈述部分回答了第一作者和布朗提出的一些问题。
英文摘要：
Let $G$ be a torsionfree compact $p$-adic analytic group. We give sufficient conditions on $p$ and $G$ which ensure that the Iwasawa algebra $Ω_G$ of $G$ has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every nonzero normal element in $Ω_G$ is a unit. We show that these conditions hold in the case when $G$ is an open subgroup of $\SL_2(\Zp)$ and $p$ is arbitrary. Using a previous result of the first author, we show that there are only two prime ideals in $Ω_G$ when $G$ is a congruence subgroup of $\SL_2(\Zp)$: the zero ideal and the unique maximal ideal. These statements partially answer some questions asked by the first author and Brown.
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