Date of Award
2009-01-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Piotr Wojciechowski
Abstract
The Riesz Decomposition Theorem for lattice ordered groups asserts that when G is an l-group and when a nonnegative element a is bounded by a product of nonnegative elements b1,...,bn, then a can be decomposed into a product of nonnegative elements b'1,...,b'n, i.e., a = b'1·...·b' n, with the property that b'i ≤ bi for any i = 1,...,n. In this work we characterize all nonnegative matrices for which this decomposition is possible with respect to matrix multiplication. In addition, we show that this result can be applied to ordered semigroups.
Language
en
Provenance
Received from ProQuest
Copyright Date
2009
File Size
50 pages
File Format
application/pdf
Rights Holder
Julio Cesar Urenda
Recommended Citation
Urenda, Julio Cesar, "Multiplicative Riesz Decomposition on the Ring of Matrices over a Totally Ordered Field" (2009). Open Access Theses & Dissertations. 373.
https://scholarworks.utep.edu/open_etd/373