| Résume | (Joint work with Kaique M.A. Roberto (IME-USP) and Hugo R.O. Ribeiro (IME-USP))
The concept of multiring was introduced by M. Marshall in 2006 and generalizes the Krasner's hyperrings (introduced in the 1950's), but multifields and hyperfields coincide. A multiring is essentially a ring with a multivalued sum satisfying a weak distributive law, but it can be viewed also as a first-order relational structure satisfying some $\forall\exists$ sentences.
In this first talk of a series, we start describing the basic notions, examples and main constructions in the category of multirings.
In the sequel, we present detailed functorial encoding of abstract theories of quadratic forms (abstract ordering spaces, (pre)special groups, real semigroups, etc) into the theory of multirings (respectively real reduced hyperfields, (pre)special hyperfields, real reduced multirings, etc).
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