草甸和划分的等式规范
Meadows and the equational specification of division
摘要：
有理数、实数和复数以及它们的标准运算，包括除法，都是由域的公理概念所指定的部分代数。由于域的类不能由方程定义，数据类型的方程规范理论不能在基于有理数、实数和复数的数系统的应用中使用域论。本文研究了一个新的公理化的概念，只使用方程的除法：草甸是一个交换环与全逆算子满足两个方程，这意味着零的逆是零。所有的田地和田地的产品都可以被看作是草地。在回顾了逆的交替公理之后，我们开始了草甸理论的发展。我们给出了Meadows的一个一般表示定理，并发现，作为推论，Meadows的条件方程理论与零总和域的条件方程理论是一致的。我们还证明了有限特征草甸的代表性结果。
英文摘要：
The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of equational specifications of data types cannot use field theory in applications to number systems based upon rational, real and complex numbers. We study a new axiomatic concept for number systems with division that uses only equations: a meadow is a commutative ring with a total inverse operator satisfying two equations which imply that the inverse of zero is zero. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms for inverse, we start the development of a theory of meadows. We give a general representation theorem for meadows and find, as a corollary, that the conditional equational theory of meadows coincides with the conditional equational theory of zero totalized fields. We also prove representation results for meadows of finite characteristic.
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