TL;DR
This paper explores the algebraic structure of quadratic rings over any base scheme, focusing on how their monoid operation relates to discriminants, providing a new perspective on their classification.
Contribution
It introduces a characterization of the monoid of quadratic rings via discriminants, offering a novel algebraic framework for understanding quadratic extensions.
Findings
The monoid of quadratic rings can be described using discriminants.
Discriminants serve as invariants that classify quadratic rings within the monoid.
The work generalizes known results to arbitrary base schemes.
Abstract
We consider the natural monoid structure on the set of quadratic rings over an arbitrary base scheme and characterize this monoid in terms of discriminants.
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