论文标题
复杂值连续功能的中间环
Intermediate rings of complex-valued continuous functions
论文作者
论文摘要
令$σ（x，\ mathbb {c}）$表示$ c^*（x，x，\ mathbb {c}）$和$ c（x，x，\ mathbb {c}）$之间的所有环的集合。我们表明，绝对凸理想/prime理想/最大理想/$ z $ -IDEALS/$ z^\ circ $ - iDeals in Rings $ p（x，x，\ mathbb {c}）$ in $σ（x，x，x，mathbb {c}）$和他们的real-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courter-courterparts， $ p（x，\ mathbb {c}）\ cap c（x）$。结果表明，任何此类$ p（x，\ mathbb {c}）$的结构空间是$βx$。我们表明，对于任何最大的理想$ m $中的$ c（x，\ mathbb {c}）），c（x，\ mathbb {c}}）/m $是代数封闭的字段。我们为理想的$ c _ {\ mathcal {p}}（x，x，\ mathbb {c}）$ $ c（x，x，\ mathbb {c}）$提供了必要和充分的条件，使其成为一个理想的理想，我们在此后检查一些特殊情况。
Let $Σ(X,\mathbb{C})$ denote the collection of all the rings between $C^*(X,\mathbb{C})$ and $C(X,\mathbb{C})$. We show that there is a natural correlation between the absolutely convex ideals/ prime ideals/maximal ideals/$z$-ideals/$z^\circ$-ideals in the rings $P(X,\mathbb{C})$ in $Σ(X,\mathbb{C})$ and in their real-valued counterparts $P(X,\mathbb{C})\cap C(X)$. It is shown that the structure space of any such $P(X,\mathbb{C})$ is $βX$. We show that for any maximal ideal $M$ in $C(X,\mathbb{C}), C(X,\mathbb{C})/M$ is an algebraically closed field. We give a necessary and sufficient condition for the ideal $C_{\mathcal{P}}(X,\mathbb{C})$ of $C(X,\mathbb{C})$ to be a prime ideal, and we examine a few special cases thereafter.
