论文标题
通勤环的绝对整体封闭
Absolute integral closures of commutative rings
论文作者
论文摘要
探索了一般交换Unital环的绝对整体封闭。所有戒指都承认绝对不可或缺的封闭，但总的来说它们并不独特。在有限的最低素数理想的降低环中，域的有限产物是它们独特的唯一环。使用模型理论的参数表明，所有无限环是连接环的有限产物的同样存在。包含给定环的每个AIC的通用绝对积分封闭事物被证明存在于某些域产品子环。
Absolute integral closures of general commutative unital rings are explored. All rings admit absolute integral closures, but in general they are not unique. Among the reduced rings with finitely many minimal prime ideals, finite products of domains are the only rings for which they are unique. Arguments using model theory suggest that the same holds for all infinite rings that are finite products of connected rings. Universal absolute integral closures, which contain every aic of a given ring, are shown to exist for certain subrings of products of domains.
