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The Boolean ring universal over a meet semilattice

Published online by Cambridge University Press:  09 April 2009

Elliot Evans
Elliot Evans
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, 37916, U.S.A.
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Abstract

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The Boolean ring B{M} universal over a meet semilattice M is examined. It is the vector space over the two element field Z2 with base M\{0}. The Z2 linear independence of a meet subsemilattice of a Boolean ring is characterized in order theoretic terms and some ramifications of this on B[M] are considered. The space (ℱpM) of proper filters of M is shown homeomorphic to the Stone space S(B[M]) of B[M] if M has no least element, with ℱP(M) ∪ {M} and S(B[M]) homeomorphic otherwise. The congruence lattice θ(M) of M is compared to the ideal lattice ℱ(B [M]) of B [M] with best results coming if M is a tree with zero when θ (M) = ℐ (B [M]).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 402 - 415
Copyright
Copyright © Australian Mathematical Society 1977

References

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