论文标题
可计数的可计入式戒指的理想
Countable strongly annihilated ideals in commutative rings
论文作者
论文摘要
在本文中，我们介绍并研究了可计数的概念，在交换环上，尤其是在连续功能的环中，尤其是在交换环上的理想。我们表明，当且仅当它是真正的最大$ z^\ circ $ ideal时，$ c（x）$中最大的理想就可以被灭绝。事实证明，$ x $在且仅当可计数的强烈歼灭理想时才是一个几乎$ p $ - 空间，并且在x $中的任何$ x \ in x $中，只有每一个$ m_x $都是一个可计数强的理想，并且只有一个可计数的强烈歼灭的理想，并且只有当时可计算的$ z $ - 理想是重合的。我们观察到，当且仅当每个可计数强的理想均被固定时，只有几乎$ p $ -p $ x $是lindelof。我们对吉尔默和麦克亚当提出的一个问题给出了负面答案。
In this paper we introduce and study the concept of countable strongly annihilated ideal in commutative rings, in particular in rings of continuous functions. We show that a maximal ideal in $C(X)$ is countable strongly annihilated if and only if it is a real maximal $z^\circ$-ideal. It turns out that $X$ is an almost $P$-space if and only if countable strongly annihilated ideals and strongly divisible $z$-ideals coincide if and only if every $M_x$ is a countable strongly annihilated ideal, for any $x\in X$. We observe that an almost $P$-space $X$ is Lindelof if and only if every countable strongly annihilated ideal is fixed. We give a negative answer to a question raised by Gilmer and McAdam.
