Hensel’s Lemma and Some Applications
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چکیده
The purpose of this note is to record Hensel’s Lemma and a few of its immediate applications for my Math 831 class. At the end of the 19th century Hensel introduced the notion of completion into a number theoretic context in order to bring to bear techniques of analysis on some purely algebraic problems in number theory. One of his most crucial discoveries (in modern terms) was that when a ring is complete in a suitable ideal-adic topology, solutions to polynomial equations with appropriate nondegeneracy conditions exist in the ring provided solutions already exist modulo the ideal. We will concern ourselves with the case that the ring in question is a local ring.
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تاریخ انتشار 2015