函数环的商环
Rings of Quotients of Rings of Functions
AI总结：
将Johnson和Utumi引入的商环应用于完全正则空间X上的连续实值函数环C(X)，研究了最大商环Q(X)的实现及其与经典商环的关系。
摘要：
摘自原序：Johnson和Utumi最近引入的商环被应用于完全正则空间X上所有连续实值函数构成的环C(X)。设Q(X)表示C(X)的最大商环；则Q(X)可实现为X的稠密开集上所有连续函数的环（模去一个明显的等价关系）。在特殊情况下（例如，对于度量空间X），Q(X)退化为C(X)的经典商环（关于正则元构成），但一般情况下，经典商环仅是Q(X)的一个真子环。
英文摘要：
From the original PREFACE: The rings of quotients recently introduced by Johnson and Utumi are applied to the ring $C(X)$ of all continuous real-valued functions on a completely regular space $X$. Let $Q(X)$ denote the maximal ring of quotients of $C(X)$; then $Q(X)$ may be realized as the ring of all continuous functions on the dense open sets of $X$ (modulo an obvious equivalence relation). In special cases (e.g., for metric $X$), $Q(X)$ reduces to the classical ring of quotients of $C(X)$ (formed with respect to the regular elements), but in general, the classical ring is only a proper sub-ring of $Q(X)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
