### 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 |
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Pages (from-to) | 258-279 |

Number of pages | 22 |

Journal | Journal of Number Theory |

Volume | 134 |

DOIs | |

Publication status | Published - 2014 Jan |

### Fingerprint

### Keywords

- Bezoutian
- Cyclotomic field
- Integral trace form
- Primary
- Secondary

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers.** / Otake, Shuichi.

Research output: Contribution to journal › Article

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TY - JOUR

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

Y1 - 2014/1

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

UR - http://www.scopus.com/inward/record.url?scp=84884405272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884405272&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2013.07.007

DO - 10.1016/j.jnt.2013.07.007

M3 - Article

AN - SCOPUS:84884405272

VL - 134

SP - 258

EP - 279

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -