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Doubling Constructions in Lattice Theory

Published online by Cambridge University Press:  20 November 2018

Alan Day
Alan Day*
Affiliation:
Department of Mathematical Sciences Lakehead University Thunder Bay, OntarioCanada P7B 5E1
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Abstract

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This paper examines the simultaneous doubling of multiple intervals of a lattice in great detail. In the case of a finite set of W-failure intervals, it is shown that there in a unique smallest lattice mapping homomorphically onto the original lattice, in which the set of W-failures is removed. A nice description of this new lattice is given. This technique is used to show that every lattice that is a bounded homomorphic image of a free lattice has a projective cover. It is also used to give a sufficient condition for a fintely presented lattice to be weakly atomic and shows that the problem of which finitely presented lattices are finite is closely related to the problem of characterizing those finite lattices with a finite W-cover.

Keywords

06B2506B05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 252 - 269
Copyright
Copyright © Canadian Mathematical Society 1992

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