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首页> 外文期刊>Journal of algebra and its applications >Comments regarding d-ideals of certain f-rings
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Comments regarding d-ideals of certain f-rings

机译：关于某些F环的d理想的注释

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Let A be a reduced commutative f-ring with identity and bounded inversion, and let A* be its subring of bounded elements. By first observing that A is the ring of fractions of A* relative to the subset of A* consisting of elements which are units in the bigger ring, we show that the frames Did(A) and Did(A*) of d-ideals of A and A*, respectively, are isomorphic, and that the isomorphism witnessing this is precisely the restriction of the extension map I → I~e which takes a radical ideal of A* to the ideal it generates in A. Specializing to the ring RL, we show that if L is an F-frame, then the saturation quotient of Did(RL) is isomorphic to βL. We also investigate projectability properties of Did(RL) and Zid(RL), where the latter denotes the frame of z-ideals of RL. We show that Zid(RL) is flatly projectable precisely when RL is a feebly Baer ring. Quite easily, Zid(RL) is projectable if and only if L is basically disconnected. Less obvious is that Did(RL) is projectable if and only if L is cozero-complemented.
机译：设A为具有恒等式和有界倒置的归约交换f环，设A *为有界元素的子环。通过首先观察到A是相对于A *的子集的A *的分数环，该子集是由较大环中的单元组成的元素，我们证明了d-ideals的框架Did（A）和Did（A *） A *和A *的同构分别是同构的，并且见证此的同构性恰好是扩展图I→I〜e的限制，该扩展图使A *的根基理想为其在A中生成的理想。 RL，我们证明如果L是F帧，则Did（RL）的饱和商与βL同构。我们还研究了Did（RL）和Zid（RL）的可投射性，其中后者表示RL的z理想框架。我们证明Zid（RL）在RL是弱Baer环时可以精确地投影。很简单，Zid（RL）在且仅当L基本断开时才是可投影的。不太明显的是，当且仅当L是cozero-complemented时，Did（RL）是可投影的。

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