Quadratic and symmetric bilinear forms on modules with unique base over a semiring

Zur Izhakian; Louis   Rowen; Manfred Knebusch

Quadratic and symmetric bilinear forms on modules with unique base over a semiring

Zur Izhakian
, Louis Rowen
, Manfred Knebusch

Mathematical Science

Bar-Ilan University
University of Regensburg

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

10 Citations (Scopus)

19 Downloads (Pure)

Abstract

We study quadratic forms on free modules with uniquebase, the situation that arises in tropical algebra, and prove the analogof Witt’s Cancelation Theorem. Also, the tensor product of anindecomposable bilinear module (U, γ) with an indecomposable quadraticmodule (V, q) is indecomposable, with the exception of one case,where two indecomposable components arise.

Original language	English
Pages (from-to)	773-808
Number of pages	36
Journal	Documenta Mathematica
Volume	21
Publication status	Published - 31 Dec 2016

Keywords

Semirings
(semi)modules
bilinear forms
quadratic forms
symmetric forms
orthogonal decomposition

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Documenta MathematicaFinal published version, 361 KBLicence: Unspecified

https://arxiv.org/abs/1509.01039Licence: Unspecified
http://www.math.uiuc.edu/documenta/vol-21/21.htmlLicence: Unspecified

Cite this

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title = "Quadratic and symmetric bilinear forms on modules with unique base over a semiring",

abstract = "We study quadratic forms on free modules with uniquebase, the situation that arises in tropical algebra, and prove the analogof Witt{\textquoteright}s Cancelation Theorem. Also, the tensor product of anindecomposable bilinear module (U, γ) with an indecomposable quadraticmodule (V, q) is indecomposable, with the exception of one case,where two indecomposable components arise.",

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AU - Izhakian, Zur

AU - Rowen, Louis

AU - Knebusch, Manfred

PY - 2016/12/31

Y1 - 2016/12/31

N2 - We study quadratic forms on free modules with uniquebase, the situation that arises in tropical algebra, and prove the analogof Witt’s Cancelation Theorem. Also, the tensor product of anindecomposable bilinear module (U, γ) with an indecomposable quadraticmodule (V, q) is indecomposable, with the exception of one case,where two indecomposable components arise.

AB - We study quadratic forms on free modules with uniquebase, the situation that arises in tropical algebra, and prove the analogof Witt’s Cancelation Theorem. Also, the tensor product of anindecomposable bilinear module (U, γ) with an indecomposable quadraticmodule (V, q) is indecomposable, with the exception of one case,where two indecomposable components arise.

KW - Semirings

KW - (semi)modules

KW - bilinear forms

KW - quadratic forms

KW - symmetric forms

KW - orthogonal decomposition

M3 - Article

SN - 1431-0635

VL - 21

SP - 773

EP - 808

JO - Documenta Mathematica

JF - Documenta Mathematica

ER -

Quadratic and symmetric bilinear forms on modules with unique base over a semiring

Abstract

Keywords

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