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Author Craven, Thomas C. ♦ Smith, Tara L.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Abstract Theory Semiorderings ♦ Witt Ring ♦ Important Invariant ♦ Marshall Abstract Theory ♦ Abstract Preorderings ♦ Algebraic Theory ♦ Powerful Tool ♦ Quadratic Form ♦ Generated Space ♦ Abstract Theory
Abstract 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 nitely generated spaces of semiorder-ings. The morphisms between such spaces are studied, generalizing the extension of valuations for elds into this context. An important invariant for studying Witt rings is the covering number of a preordering. Covering numbers are dened for abstract preorderings and related to other invariants of the Witt ring.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study