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2015•arXiv (Cornell University)Open access

Quadratic and Symmetric Bilinear Forms on Modules with Unique Base Over\n a Semiring

Zur Izhakian, Manfred Knebusch, Louis Rowen

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Abstract

We study quadratic forms on free modules with unique base, the situation that\narises in tropical algebra, and prove the analog of Witt's Cancellation\nTheorem. Also, the tensor product of an indecomposable bilinear module $(U,\n\\gamma)$ with an indecomposable quadratic module $(V,q) $ is indecomposable,\nwith the exception of one case, where two indecomposable components arise.\n

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We study quadratic forms on free modules with unique base, the situation that\narises in tropical algebra, and prove the analog of Witt's Cancellation\nTheorem. Also, the tensor product of an indecomposable bilinear module $(U,\n\\gamma)$ with an indecomposable quadratic module $(V,q) $ is indecomposable,\nwith the exception of one case, where two indecomposable components arise.\n

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Available abstract

We study quadratic forms on free modules with unique base, the situation that\narises in tropical algebra, and prove the analog of Witt's Cancellation\nTheorem. Also, the tensor product of an indecomposable bilinear module $(U,\n\\gamma)$ with an indecomposable quadratic module $(V,q) $ is indecomposable,\nwith the exception of one case, where two indecomposable components arise.\n

Key concepts: Indecomposable module, Tensor product, Bilinear form, Base (topology), Bilinear interpolation, Mathematics, Quadratic equation, Pure mathematics

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