Topics on strict closure of rings
Topics on strict closure of rings
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DOI：
10.1007/s40687-021-00292-1
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发表时间：
2021-04
影响因子：
1.2
通讯作者：
Naoki Endo;S. Goto;Ryotaro Isobe
中科院分区：
文献类型：
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作者：
Naoki Endo;S. Goto;Ryotaro Isobe
1971年，Lipman （Am J Math 93:649-685, 1971）引入了环在另一个环中的严格闭包的概念，并结合O. Zariski的一个猜想建立了其基础理论。在本文中，为了进一步发展这一理论，我们研究了与环的严格闭包有关的三个不同的主题。第一个问题是关于闭包的构造，第二个问题是关于在平同态下严格闭包是否继承的问题。我们最终处理了Arf关闭与严格关闭何时重合的问题。我们用例子来说明我们的定理。
In 1971, Lipman (Am J Math 93:649–685, 1971) introduced the notion of strict closure of a ring in another, and established the underlying theory in connection with a conjecture of O. Zariski. In this paper, for further developments of the theory, we investigate three different topics related to strict closure of rings. The first one concerns construction of the closure, and the second one is the study regarding the question of whether the strict closedness is inherited under flat homomorphisms. We finally handle the question of when the Arf closure coincides with the strict closure. Examples are explored to illustrate our theorems.