In this paper, new algebraic and topological results on purely-prime ideals of a commutative ring are obtained. Some applications of this study are also given. In particular, the new notion of semi-noetherian ring is introduced and Cohen type theorem is proved.

中文翻译：

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关于具有应用的纯素理想

在本文中，获得了交换环纯素理想的新代数和拓扑结果。还给出了本研究的一些应用。特别是，引入了半诺以太环的新概念并证明了科恩型定理。