论文标题
通勤环的无限产品中的主要理想
Prime ideals in infinite products of commutative rings
论文作者
论文摘要
我们描述了产品$ r = \ prodd_λ$的最大理想$（d_λ）_ {λ\inλ} $的最大理想。我们表明，在布尔代数$ \ prod \ prod \ mathcal {p}（\ max（d_λ））$上的超级滤器引起了每个最大理想，其中$ \ max（d_λ）$是$d_λ$的最大理想的频谱，$d_λ$，$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {p}。如果每个$d_λ$都在某个类别的环中，包括有限字符域和一维域，我们完全表征了$ r $的最大理想。如果每个$d_λ$都是prüfer域，我们将完全表征$ r $的所有主要理想。
We describe the prime ideals and, in particular, the maximal ideals in products $R = \prod D_λ$ of families $(D_λ)_{λ\in Λ}$ of commutative rings. We show that every maximal ideal is induced by an ultrafilter on the Boolean algebra $\prod \mathcal{P}(\max(D_λ))$, where $\max(D_λ)$ is the spectrum of maximal ideals of $D_λ$, and $\mathcal{P}$ denotes the power set. If every $D_λ$ is in a certain class of rings including finite character domains and one-dimensional domains, we completely characterize the maximal ideals of $R$. If every $D_λ$ is a Prüfer domain, we completely characterize all prime ideals of $R$.
