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1 results

  • Doubling Constructions in Lattice Theory

  • Alan Day
  • Journal:
    Canadian Journal of Mathematics / Volume 44 / Issue 2 / 01 April 1992
    Published online by Cambridge University Press:
    20 November 2018, pp. 252-269
    Print publication:
    01 April 1992
    • Article
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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.