Electronic Resource
Springer
Order
10 (1993), S. 77-92
ISSN:
1572-9273
Keywords:
06B05
;
06B20
;
Doubling construction
;
semidistributive lattices
;
k-semidistributivity
;
context
;
doubling classes
;
pseudovariety
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A latticeL is called congruence normal if it can be generated by doubling of convex sets starting with the one-element lattice. In the special case of intervals, the lattice is called bounded. It has been proven thatL is bounded if and only ifL is congruence normal and semidistributive. In this paper we study the connection between certain classes of convex sets and generalized semidistributive laws. These so-called doubling classes are pseudovarieties which can be described by implications as well as by forbiden substructures. In the end, we examine the structure of the lattice of all doubling classes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01108710
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