On a characterization of the maximal ideal spaces of algebraically closed commutative *-algebras
On a characterization of the maximal ideal spaces of algebraically closed commutative *-algebras
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代数闭交换*-代数的最大理想空间的刻画
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发表时间：
2002
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通讯作者：
Kazuki Niijima
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作者：
T. Miura;Kazuki Niijima
设C(X)是紧Hausdorff空间X上所有复值连续函数的代数，如果C(X)上的每个一元多项式方程都有连续解，则称C(X)是代数闭的。给出了局部连通紧Hausdorff空间X上C(X)是代数闭的一个充要条件，证明了当C(X)的每个元素都是另一个元素的平方时，C(X)是代数闭的.给出了第一可数紧Hausdorff空间X的一个特征，使得C(X)是代数闭的。
Let C(X) be the algebra of all complex-valued continuous functions on a compact Hausdorff space X. We say that C(X) is algebraically closed if each monic polynomial equation over C(X) has a continuous solution. We give a necessary and sufficient condition for C(X) to be algebraically closed for a locally connected compact Hausdorff space X. In this case, it is proved that C(X) is algebraically closed if each element of C(X) is the square of another. We also give a characterization of a first-countable compact Hausdorff space X such that C(X) is algebraically closed.
O.Hatori：“关于交换 C^* 代数的最大理想空间的表征，其中每个元素”
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