Volume 16, Number 1, January 2022, 105-141.
https://doi.org/10.52547/cgasa.16.1.105
Quadratic structures associated to
(multi)rings
K.M.d.A. Roberto, H.R.d.O. Ribeiro, and H.L. Mariano
∗
Abstract. We consider certain pairs (A, T ) where A is a (multi)ring and
T ⊆ A is a multiplicative set that generates, by a convenient quotient con-
struction, a (multi)structure that supports a quadratic form theory: with
some natural hypotheses we generalize constructions previously presented
in [3] and [6]. This also provides some steps towards an abstract formally
real quadratic form theory (non necessarily reduced) were the forms have
general coefficients (non only units).
1 Introduction
In [3], [5] and [6] are considered abstract theories of quadratic forms: spe-
cial groups and real semigroups. The former treats simultaneously reduced
and non-reduced theories but focuses on rings with a good amount of in-
vertible coefficients to quadratic forms. The latter has the advantage of
potentially consider general coefficients of a ring, but only addresses the
* Corresponding author
Keywords : Quadratic forms, special groups, real semigroup, multirings, hyperfields.
Mathematics Subject Classification [2010]: 11Exx, 11E81.
Received: 16 January 2021, Accepted: 15 May 2021.
ISSN: Print 2345-5853, Online 2345-5861.
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