International Journal of Mathematics and Mathematical Sciences (Jan 2012)

Noetherian and Artinian Lattices

  • Derya Keskin Tütüncü,
  • Sultan Eylem Toksoy,
  • Rachid Tribak

DOI
https://doi.org/10.1155/2012/157169
Journal volume & issue
Vol. 2012

Abstract

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It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.