In:
International Journal of Number Theory, World Scientific Pub Co Pte Ltd, Vol. 15, No. 01 ( 2019-02), p. 89-103
Abstract:
Let [Formula: see text] be a number field of degree [Formula: see text] over [Formula: see text] and [Formula: see text] its ring of integers. For a prime number [Formula: see text], we determine the types of splittings of [Formula: see text] in [Formula: see text] for which the set [Formula: see text] is of cardinality a power of [Formula: see text]. We prove that this necessary condition is also sufficient for [Formula: see text] to be a subgroup of the additive group [Formula: see text]. Consequently, we show that, in this case, the subset of [Formula: see text] , [Formula: see text] is an order of the number field.
Type of Medium:
Online Resource
ISSN:
1793-0421
,
1793-7310
DOI:
10.1142/S1793042118501750
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2019
SSG:
17,1
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