ISSN:
1572-9273
Keywords:
Primary: 06A10, 06A12, 06F99
;
secondary: 04A10, 04A20, 06B05, 06F05
;
Partially ordered algebra
;
disjoint cofinal subalgebras
;
lattice
;
semilattice
;
cofinality (resp. global cofinality) of a partially ordered set
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 α then there exists a family of α 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00383602
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