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

Zur Izhakian; Manfred Knebusch; Louis Rowen

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

Zur Izhakian
, Manfred Knebusch
, Louis Rowen

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

10 Scopus citations

Abstract

We study quadratic forms on free modules with unique base, the situation that arises in tropical algebra, and prove the analog of Witt's Cancelation Theorem. Also, the tensor product of an indecomposable bilinear module (U, γ) with an indecomposable quadratic module (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
Issue number	2016
State	Published - 2016
Externally published	Yes

Keywords

(semi)modules
Bilinear forms
Orthogonal decomposition
Quadratic forms
Semirings
Symmetric forms

Cite this

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

KW - (semi)modules

KW - Bilinear forms

KW - Orthogonal decomposition

KW - Quadratic forms

KW - Semirings

KW - Symmetric forms

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

Abstract

Keywords

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