Vol. 283, No. 2, 2016

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ISSN: 0030-8730
Discriminants and the monoid of quadratic rings

John Voight

Vol. 283 (2016), No. 2, 483–510
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.

Keywords
quadratic forms, quadratic rings, monoids, discriminants, discriminant algebras
Mathematical Subject Classification 2010
Primary: 11E99
Secondary: 11R11, 11R29
Milestones
Received: 8 May 2015
Revised: 12 February 2016
Accepted: 12 February 2016
Published: 22 June 2016
Authors
John Voight
Department of Mathematics
Dartmouth College
6188 Kemeny Hall
Hanover, NH 03755
United States