布尔度量空间与布尔algebraic varieties
Boolean metric spaces and Boolean algebraic varieties
摘要：
利用布尔度量空间和凸组合的概念刻画了一类交换VonNeumann正则环（包括布尔环和p-环，我们称之为CFG-环）中的多项式映射.在这些环中，研究代数簇范畴（即有限个多项式方程的解的集合，多项式映射作为态射）等价于研究一类布尔度量空间，我们在这里称之为CFG-空间。
英文摘要：
The concepts of Boolean metric space and convex combination are used to characterize polynomial maps in a class of commutative Von Neumann regular rings including Boolean rings and p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.
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