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

### Summary

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.

### Mathematics Subject Classification

15A03, 15A09, 15A15, 16Y60, 14T05, 15A33, 20M18, 51M20

### Keywords/Phrases

semirings, (semi)modules, bilinear forms, quadratic forms, symmetric forms, orthogonal decomposition