If you are experiencing problems downloading PDF or HTML fulltext, our helpdesk recommend clearing your browser cache and trying again. If you need help in clearing your cache, please click here . Still need help? Email help@ingentaconnect.com

Partial Fields and Matroid Representation

The full text article is not available for purchase.

The publisher only permits individual articles to be downloaded by subscribers.

Abstract:

A partial field P is an algebraic structure that behaves very much like a field except that addition is a partial binary operation, that is, for some a , b∈ P , a + b may not be defined. We develop a theory of matroid representation over partial fields. It is shown that many important classes of matroids arise as the class of matroids representable over a partial field. The matroids representable over a partial field are closed under standard matroid operations such as the taking of minors, duals, direct sums, and 2-sums. Homomorphisms of partial fields are defined. It is shown that if varphi: P 1 -< P 2 is a non-trivial partial-field homomorphism, then every matroid representable over P 1 is representable over P 2 . The connection with Dowling group geometries is examined. It is shown that if G is a finite abelian group, and r >2, then there exists a partial field over which the rank- r Dowling group geometry is representable if and only if G has at most one element of order 2, that is, if G is a group in which the identity has at most two square roots.

Document Type: Research Article

Affiliations: Department of Mathematics, Victoria University, Wellington, New Zealand

Publication date: June 1, 1996

Related content

Tools

Favourites

Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more