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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Witt rings and matroids


Authors: Thomas C. Craven and Zachary A. Kent
Journal: Proc. Amer. Math. Soc. 141 (2013), 1505-1517
MSC (2010): Primary 13M05; Secondary 12D15, 11E81
Published electronically: October 11, 2012
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Abstract: The study of Witt rings of formally real fields in the algebraic theory of quadratic forms has led to a particularly good understanding of the finitely generated torsion free Witt rings. In this paper, we work primarily with a somewhat more general class of rings which can be completely characterized by (binary) matroids. The different types of standard constructions and invariants coming from algebra and from combinatorics lead to previously unstudied problems for both areas; in particular, there are new invariants for Witt rings and new constructions for matroids with many open questions.


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Additional Information

Thomas C. Craven
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: tom@math.hawaii.edu

Zachary A. Kent
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: kent@mathcs.emory.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11428-5
PII: S 0002-9939(2012)11428-5
Received by editor(s): August 29, 2011
Published electronically: October 11, 2012
Communicated by: Ken Ono
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.