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Algebraic function fields and non-standard analysis. (English) Zbl 1346.03052

Summary: Non-standard analysis was developed in 1960–1970 as an application of logical methods to such topic as abstract algebra, analysis field theory. The present work considers applications of non-standard analysis to modern algebra. It is based on A. Robinson’s work [in: Contribution to non-standard analysis. London: North-Holland Publishing Company. 1–14 (1972; Zbl 0247.12107)]. A possibility of generalizing Robinson’s argument is considered. Some other applications of non-standard analysis to algebra include, for example, applications of non-standard methods, computational group theory and the theory of rewrite rules.

MSC:

03H05 Nonstandard models in mathematics
12L15 Nonstandard arithmetic and field theory
14H05 Algebraic functions and function fields in algebraic geometry

Citations:

Zbl 0247.12107
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