Small lattices

Date
2000
Authors
Heeney, Xiang Xia Huang
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Freese, Ralph
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University of Hawaii at Manoa
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Abstract
This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple gluing irreducible [Special characters omitted.] lattices are introduced. The conditions which insure [Special characters omitted.] small are discovered. This dissertation also give some triple gluing irreducible small lattices by gluing [Special characters omitted.] 's. Finally, K-structured lattices are introduced. We prove that a K-structured lattice L is triple gluing irreducible if and only if [Special characters omitted.] . We prove that no 4-element antichain lies in u 1 /v1 of a K-structured small lattice. We also prove that some special lattices with 3-element antichains can not lie in u1 /v1 of a K-structured small lattice.
Description
viii, 87 leaves, bound : ill. ; 29 cm.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2000.
Keywords
Lattice theory.
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viii, 87 leaves
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Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Mathematics ; no. 3928
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