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0-Distributive and P-Uniform Semilattices

Published online by Cambridge University Press:  20 November 2018

C. S. Hoo
Affiliation:
University of Alberta, Edmonton, Alberta, Canada
K. P. Shum
Affiliation:
Chinese University of Hong Kong, Shatin, N.T. Hong Kong
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Abstract

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A counter-example is provided to the conjecture of Y. S. Pawar and N. K. Thakare that a semilattice S with 0 is 0-distributive if and only if for each filter F and each ideal I such that FI = Ø, there exists a prime filter containing F and disjoint from I. This shows that 0-distributivity is not equivalent to weak distributivity. A characterization is also given of finite P-uniform semilattices in terms of 0-distributivity.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1982

References

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