ISSN:
1572-9273
Keywords:
Primary 06A12
;
secondary 06A10
;
Semilattice
;
descending chain condition
;
branching
;
dimension
;
rank
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Given a maximal subchainC of a semilatticeS, there are some natural ‘leaves’ ofS attached to it. These are subsemilattices ofS which may have a simpler structure thanS itself. We look atS as build up fromC together with its leaves. Starting with one-point subsemilattices, the ‘(branching) rank’ ofS is defined to be the least number of steps needed to recoverS. For technical reasons, only semilattices with no infinite descending chains are considered. The main result states that ifR is a subsemilattice ofS and rankS is defined, then rankR≤rankS. On the other hand, rank does not behave well with respect to epimorphisms. Several examples are presented as well as various results concerning finite semilattices and trees.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00714480
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