Quadratic structures associated to (multi)rings

We consider certain pairs (A, T) where A is a (multi)ring andT ⊆ A is a multiplicative set that generates, by a convenient quotient construction,a (multi)structure that supports a quadratic form theory: withsome natural hypotheses we generalize constructions previously presentedin [۳] and [۶]. This also provides some steps towards an abstract formallyreal quadratic form theory (non necessarily reduced) were the forms havegeneral coefficients (non only units).

Keywords:

quadratic forms , special groups , real semigroup , multirings , hyperfields