A cofinal coloring theorem for partially ordered algebras |
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| Authors: | George M. Bergman Irving Kaplansky |
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| Affiliation: | (1) Department of Mathematics, University of California, 94720 Berkeley, CA, USA;(2) Mathematical Sciences Research Institute, 2223 Fulton St., 94720 Berkeley, CA, USA;(3) Department of Mathematics, University of California, 94720 Berkeley, CA, USA |
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| Abstract: | If P is a directed partially ordered algebra of an appropriate sort-e.g. an upper semilattice-and has no maximal element, then P has two disjoint subalgebras each cofinal in P. In fact, if P has cofinality  then there exists a family of such disjoint subalgebras. A version of this result is also proved without the directedness assumption, in which the cofinality of P is replaced by an invariant which we call its global cofinality.This work was done while the first author was partly supported by NSF contract MCS 82-02632. |
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| Keywords: | Primary: 06A10, 06A12, 06F99 secondary: 04A10, 04A20, 06B05, 06F05 |
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