Geodesic
Quadratic and symmetric bilinear forms on modules with unique base over a semiring
Documenta mathematica, Tome 21 (2016), pp. 773-808.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $(U, \gm)$ with an indecomposable quadratic module $(V,q) $ is indecomposable, with the exception of one case, where two indecomposable components arise.
Classification : 15A03, 15A09, 15A15, 16Y60, 14T05, 15A33, 20M18, 51M20
Keywords: semirings, (semi)modules, bilinear forms, quadratic forms, symmetric forms, orthogonal decomposition 
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     title = {Quadratic and symmetric bilinear forms on modules with unique base over a semiring},
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Izhakian, Zur; Knebusch, Manfred; Rowen, Louis. Quadratic and symmetric bilinear forms on modules with unique base over a semiring. Documenta mathematica, Tome 21 (2016), pp. 773-808. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a23/