ISSN:
1572-9273
Keywords:
06A06
;
fixed point
;
irreducible element
;
dismantlability
;
core
;
N-free
;
retractible element
;
four crown tower
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract When does the fixed point property of a finite ordered set imply its dismantlability by irreducible elements? For instance, if it has width two. Although every finite ordered set is dismantlable by retractible (not necessarily irreducible) elements, surprisingly, a finite, dimension two ordered set, need not be dismantlable by irreducible elements. If, however, a finite ordered set with the fixed point property is N-free and of dimension two, then it is dismantlable by irreducibles. A curious consequence is that every finite, dimension two ordered set has a complete endomorphism spectrum.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00338744
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