scholarly journals Some Aspects of the Algebraic Theory of Quadratic Forms

2013 ◽  
pp. 181-205
Author(s):  
R. Parimala
Keyword(s):  
Quadratic Forms ◽  
Algebraic Theory

Geometric Methods in the Algebraic Theory of Quadratic Forms

2004 ◽  
Author(s):  
Oleg T. Izhboldin ◽  
Bruno Kahn ◽  
Nikita A. Karpenko ◽  
Alexander Vishik
Keyword(s):  
Quadratic Forms ◽  
Algebraic Theory ◽  
Geometric Methods

scholarly journals A class of finite commutative rings constructed from Witt rings

2006 ◽  
Vol 73 (1) ◽  
pp. 47-64 ◽  
Author(s):  
Thomas Craven ◽  
Monika Vo
Keyword(s):  
Quadratic Forms ◽  
Special Class ◽  
Algebraic Theory ◽  
Commutative Rings ◽  
Group Rings ◽  
Integral Group ◽  
Witt Rings ◽  
Integral Group Rings ◽  
Quotient Rings ◽  
Finite Commutative Rings

Motivated by constructions of Witt rings in the algebraic theory of quadratic forms, the authors construct new classes of finite commutative rings and explore some of their properties. These rings are constructed as quotient rings of a special class of integral group rings for which the group is an elementary 2-group. The new constructions are compared to other rings in the literature.

scholarly journals Abstract theory of semiorderings

2005 ◽  
Vol 72 (2) ◽  
pp. 225-250
Author(s):  
Thomas C. Craven ◽  
Tara L. Smith
Keyword(s):  
Quadratic Forms ◽  
Algebraic Theory ◽  
Covering Number ◽  
Finitely Generated ◽  
Abstract Theory ◽  
Witt Ring ◽  
Witt Rings ◽  
Covering Numbers ◽  
Spaces Of Orderings

Marshall's abstract theory of spaces of orderings is a powerful tool in the algebraic theory of quadratic forms. We develop an abstract theory for semiorderings, developing a notion of a space of semiorderings which is a prespace of orderings. It is shown how to construct all finitely generated spaces of semiorderings. The morphisms between such spaces are studied, generalising the extension of valuations for fields into this context. An important invariant for studying Witt rings is the covering number of a preordering. Covering numbers are defined for abstract preorderings and related to other invariants of the Witt ring.

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