The Fields $${\mathbb {Q}}_p$$ Q p of p-Adic Numbers: Hensel’s Lemma

Benjamin Fine () and Gerhard Rosenberger
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Benjamin Fine: Fairfield University, Department of Mathematics
Gerhard Rosenberger: Universität Hamburg

Chapter Chapter 7 in Number Theory, 2016, pp 371-404 from Springer

Abstract: Abstract In the previous chapter, we described algebraic extensions of the rational numbers. We then saw that the arithmetic of the integers within these algebraic number fields was similar to that of the ordinary integers and further that many algebraic number fields allowed unique factorization while all these fields allowed unique factorization in terms of ideals.

Keywords: Algebraic Number Field; Unique Factorization Domain; Cauchy Sequence; Cauchy Completion; Discrete Valuation field (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-43875-7_7

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