Computable algebra, general theory and theory of computable fields.
Computable algebra, general theory and theory of computable fields.
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可计算代数、一般理论和可计算域理论。
DOI：
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发表时间：
1960
期刊：
影响因子：
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通讯作者：
M. Rabin
中科院分区：
文献类型：
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作者：
M. Rabin
代数是从整数环或有理数域这样的具体系统到相应的、公理定义的抽象系统的过渡的产物。在这个抽象的过程中，具体系统的各种属性都会丢失。例如，有理数域具有自然的拓扑、有序，而且域运算，即有理数的加法和乘法，是有效的可计算函数。这些属性都不包含在字段的公理定义中。人们进行了各种尝试，试图将这些特征中的一些重新纳入代数系统的研究中。在拓扑代数中，我们研究具有拓扑的群，条件是代数运算是关于这个拓扑的连续函数。基本定义
algebra is the product of a transition from such concrete systems as the ring of integers or the field of rational numbers to the corresponding, axiomatically defined, abstract systems. In the course of this abstraction process various properties of the concrete system are lost. The field of rational numbers, for example, possesses a natural topology, an ordering, and furthermore the field operations, that is addition and multiplication of rationals, are effectively computable functions. None of these properties enters into the axiomatic definition of a field. Various attempts were made to reincorporate some of these features into the study of algebraic systems. In topological algebra we study groups endowed with a topology subject to the condition that the algebraic operations are continuous functions with respect to this topology. The basic definitions