An Introduction To Partially Ordered Structures And Sheaves
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Ordered Algebraic Structures and Related Topics
Author: Fabrizio Broglia
language: en
Publisher: American Mathematical Soc.
Release Date: 2017
Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Faithfully Quadratic Rings
Author: M. Dickmann
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-10-27
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.