Journal of Mathematics and Statistics

Homomorphisms on Lattices of Measures

Norris Sookoo and Peter Chami

DOI : 10.3844/jmssp.2009.276.282

Journal of Mathematics and Statistics

Volume 5, Issue 4

Pages 276-282

Abstract

Problem statement: Homomorphisms on lattices of measures defined on the quotient spaces of the integers were considered. These measures were defined in terms of Sharma-Kaushik partitions. The homomorphisms were studied in terms of their relationship with the underlying Sharma-Kaushik partitions. Approach: We defined certain mappings between lattices of Sharma-Kaushik partitions and showed that they are homomorphisms. These homomorphisms were mirrored in homorphisms between related lattices of measures. Results: We obtained the structure of certain homomorphisms of measures. Conclusion: Further information about homomorphisms between lattices of measures of the type considered here can be obtained by investigating the underlying lattices of Sharma-Kaushik partitions.

Copyright

© 2009 Norris Sookoo and Peter Chami. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.