Geodesic
Quadratic and symmetric bilinear forms on modules with unique base over a semiring
Documenta mathematica, Tome 21 (2016), pp. 773-808
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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.
DOI : 10.4171/dm/545
Classification : 15A03, 15A09, 15A15, 16Y60, 20M18, 51M20
Mots-clés : quadratic forms, semirings, (semi)modules, bilinear forms, symmetric forms, orthogonal decomposition 
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     author = {Louis Rowen and Zur Izhakian and Manfred Knebusch},
     title = {Quadratic and symmetric bilinear forms on modules with unique base over a semiring},
     journal = {Documenta mathematica},
     pages = {773--808},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/545},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/545/}
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Louis Rowen; Zur Izhakian; Manfred Knebusch. Quadratic and symmetric bilinear forms on modules with unique base over a semiring. Documenta mathematica, Tome 21 (2016), pp. 773-808. doi: 10.4171/dm/545

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