Research Article Open Access

Homomorphisms on Lattices of Measures

Norris Sookoo and Peter Chami

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.

Journal of Mathematics and Statistics
Volume 5 No. 4, 2009, 276-282

DOI: https://doi.org/10.3844/jmssp.2009.276.282

Submitted On: 25 May 2009 Published On: 31 December 2009

How to Cite: Sookoo, N. & Chami, P. (2009). Homomorphisms on Lattices of Measures. Journal of Mathematics and Statistics, 5(4), 276-282. https://doi.org/10.3844/jmssp.2009.276.282

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Keywords

  • Measure
  • lattice
  • ideal
  • partition