Orders with a normal basis

Kostra, Juraj

doi:10.21136/cmj.1985.102029

Czech. Math. J.

1985

DOI: 10.21136/cmj.1985.102029

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Orders with a normal basis

Juraj Kostra¹

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

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2013

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Properties of transformation matrices between the normal bases in orders of cubic field

Václavíková

2013

Mathematica Slovaca

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ABSTRACT. In this paper, the properties of transformation matrices between the normal bases in orders of algebraic number fields of degree 3 are shown. Let K be a finite extension of the rational number field Q and let the Z K be integral closure of the ring Z in K -i.e. the ring of integral numbers of the field K.Ò Ø ÓÒ 1º Let K be an algebraic number field of degree n over the rational numbers Q. A Z-module B ⊂ K is called an order of the field K if B satisfies the following conditions:(2) B has a basis over Z consisting of n elements, (3) B is ring.Let K be a cyclic algebraic number field of degree n over Q. Such a field has a normal basis over Q, i.e. a basis which consists of all conjugations of one element.Transformation matrices between two normal bases of K over Q are exactly regular rational circulant matrices of degree n.In

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Properties of transformation matrices between the normal bases in orders of cubic field

Václavíková

2013

Mathematica Slovaca

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Orders with a normal basis

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 1 publication

References 0 publications

Properties of transformation matrices between the normal bases in orders of cubic field

Properties of transformation matrices between the normal bases in orders of cubic field

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