A Characterization for non-DCC Lattices
Abstract
Join-irreducible elements in a lattice have an important
role. They act like blocks of a lattice. In DCC lattices each element of
the lattice has a unique finite representation as a join of join-irreducible
elements. In this paper, we seek lattices which contains elements that
can be represented as an infinite supremum of join-irreducible elements.
One of these lattices is the lattice of sequences. Finally, we give a new
characterization for such lattices
role. They act like blocks of a lattice. In DCC lattices each element of
the lattice has a unique finite representation as a join of join-irreducible
elements. In this paper, we seek lattices which contains elements that
can be represented as an infinite supremum of join-irreducible elements.
One of these lattices is the lattice of sequences. Finally, we give a new
characterization for such lattices
Keywords
Lattice, join-irreducible element, completely
join-irreducible element, DCC, compactly generated
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