Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

Shuichi Otake

doi:10.1016/j.jnt.2013.07.007

Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

Shuichi Otake^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζn)/Q to OQ(ζn) and we get orthogonal decompositions of symmetric Z-bilinear modules OQ(ζn) into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric Zp-bilinear modules Zp⊗ZOQ(ζn) over Zp the ring of p-adic integers.

Original language	English
Pages (from-to)	258-279
Number of pages	22
Journal	Journal of Number Theory
Volume	134
DOIs	https://doi.org/10.1016/j.jnt.2013.07.007
Publication status	Published - 2014 Jan

Keywords

Bezoutian
Cyclotomic field
Integral trace form
Primary
Secondary

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2013.07.007

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title = "Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers",

abstract = "In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζn)/Q to OQ(ζn) and we get orthogonal decompositions of symmetric Z-bilinear modules OQ(ζn) into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric Zp-bilinear modules Zp⊗ZOQ(ζn) over Zp the ring of p-adic integers.",

keywords = "Bezoutian, Cyclotomic field, Integral trace form, Primary, Secondary",

author = "Shuichi Otake",

year = "2014",

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doi = "10.1016/j.jnt.2013.07.007",

language = "English",

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pages = "258--279",

journal = "Journal of Number Theory",

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T1 - Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

AU - Otake, Shuichi

PY - 2014/1

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N2 - In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζn)/Q to OQ(ζn) and we get orthogonal decompositions of symmetric Z-bilinear modules OQ(ζn) into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric Zp-bilinear modules Zp⊗ZOQ(ζn) over Zp the ring of p-adic integers.

AB - In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζn)/Q to OQ(ζn) and we get orthogonal decompositions of symmetric Z-bilinear modules OQ(ζn) into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric Zp-bilinear modules Zp⊗ZOQ(ζn) over Zp the ring of p-adic integers.

KW - Bezoutian

KW - Cyclotomic field

KW - Integral trace form

KW - Primary

KW - Secondary

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M3 - Article

AN - SCOPUS:84884405272

SN - 0022-314X

VL - 134

SP - 258

EP - 279

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

Abstract

Keywords

ASJC Scopus subject areas

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