Subordinate quadratic forms and isometric maps over semirings

Abstract

This paper expands the theory of quadratic forms on modules over a semiring [Formula: see text], introduced in [11–13], especially in the setup of tropical and supertropical algebra. Isometric linear maps induce subordination on quadratic forms, and provide a main tool in our current study. These maps allow lifts and pushdowns of quadratic forms on different modules, preserving basic characteristic properties.