On cerrain classes of pe-rings
On cerrain classes of pe-rings
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DOI：
10.1080/00927878408823063
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发表时间：
1984
影响因子：
0.7
通讯作者：
M. Contessa
中科院分区：
文献类型：
--
作者：
M. Contessa
介绍。最近在[5]中研究了pm-环类（其中每个素理想都包含在一个唯一的极大理想中）和tb-环类（其中极大谱是一个布尔拓扑空间），本工作是对这类研究的延续。理想情况下，我们希望将任何环都与万向pm环联系起来。由于这在一般情况下似乎是极其困难的，我们将考虑一些特殊类型的pm-ring的相同问题，例如53的C-ningh（结果与$2的tb-ring一致）；赢得了54的Neumann & c& tLingb（直接产品下未关闭的一类）。在第55节中，我们介绍并研究了d指类。在56中进行的更深入的研究将我们引向定理6.10，它部分地实现了我们的目标。事实上，对于任意环A，我们能够构造一个唯一的包含A且包含在直积-/-/- am中的“极小”d环A。我们称A为canov~ &~ & D-enveRope tx3faxA 1447
INTRODUCTION. The class of pm-rings (firzgb inwhich every prime ideal is contained in a unique maximal ideal) and the class of tb-rings (ning6 for which the maximal spectrum is a boolean topological space) have recently been studied in [5] and the present work is a continuation. Ideally we would like to associate with any ring a universal pm-ring. Since this appears to be extremely difficult in general, we shall consider the same problem for some special types of pm-rings, for example the C-ningh of 53 (which turn out to coincide with the tb-rings of $2); the won Neumann &uc& tLingb of 54 (a class which is not closed under direct products). In 55 we introduce and study the class of D-fingb. A deeper investigation made in 56 leads us to Theorem 6.10 which partially fulfills our goal. In fact, we are able to construct for an arbitrary ring A a unique" minimal" D-ring A" containing A and contained in the direct product-/-/-Am. We call A' the canov~ &~ & D-enveRope tx3faxA 1447