论文标题
关于理想的回避财产
On the ideal avoidance property
论文作者
论文摘要
在本文中，我们调查了理想和戒指的回避属性。在主要结果中，制定了回避引理的一般版本。结果表明，每个基本的理想（因此，每个纯粹的理想）都有避免。特征是任意直接避免环的避免属性。结果表明，避免域的每一个过度范围都是回避域。接下来，我们证明每一个回避$ \ mathbb {n} $ - 分级环的基础子串是有限的字段，就是PIR。还证明，避难所保留在平圆环的表达下。双重地，我们制定了一个强烈回避的概念，并表明它是由纯粹的形态反映的。
In this article, we investigate the avoidance property of ideals and rings. Among the main results, a general version of the avoidance lemma is formulated. It is shown that every idempotent ideal (and hence every pure ideal) has avoidance. The avoidance property of arbitrary direct products of avoidance rings is characterized. It is shown that every overring of an avoidance domain is an avoidance domain. Next, we show that every avoidance $\mathbb{N}$-graded ring whose base subring is a finite field is a PIR. It is also proved that the avoidance property is preserved under flat ring epimorphisms. Dually, we formulate a notion of strong avoidance, and show that it is reflected by pure morphisms.
