Orders in a Field

David Hilbert

Chapter 9 in The Theory of Algebraic Number Fields, 1998, pp 67-75 from Springer

Abstract: Abstract Let υ, η, ... be any algebraic integers whose domain of rationality is the field k l of degree m; then the set of all polynomials in ϑ, η, ... with rational integer coefficients is called an order 2. Addition, subtraction and multiplication of two numbers in an order produce again numbers in the order. An order is thus invariant under the three operations of addition, subtraction and multiplication. The maximal order in a field k is the order determined by ω 1, ... ω m where these are numbers of a basis for k; this consists of all the algebraic integers of k.

Keywords: Lattice Class; Algebraic Number; Great Common Divisor; Order Ideal; Algebraic Integer (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-3-662-03545-0_9

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