A Characterization for non-DCC Lattices

Authors

  • Mahboobeh Hosseinyazdi
  • Amin Ghanbarnezhad

Keywords:

Lattice, join-irreducible element, completely join-irreducible element, DCC, compactly generated

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

Author Biographies

Mahboobeh Hosseinyazdi

Department of Mathematics Payame Noor University(PNU) Shiraz, Iran.

Amin Ghanbarnezhad

Department of Mathematics Payame Noor University(PNU) Shiraz, Iran.

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Published

2009-03-02

Issue

Vol 3 (2008-2009)

Section

Vol. 3, No. 2 (2009)

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