Iosif, Mihai Some remarks on modular QFD lattices. (English) Zbl 1150.06009 Rev. Roum. Math. Pures Appl. 52, No. 3, 341-347 (2007). The aim of the present paper is to prove for lattices some results which come from module theory. The main result of the paper is Proposition 1.6, a characterization of upper continuous modular lattices which are compactly generated and QFD (i.e., every interval \([x,1]\) has no infinite independent subsets). This result is applied to Grothendieck categories in Proposition 3.11. Another interesting result is Proposition 2.10, which provides a sufficient condition for the existence of dual Krull dimension for the poset of all subdirectly irreducible elements of an interval \([a,b]\) in an almost compactly generated modular lattice. Reviewer: Simion Sorin Breaz (Cluj-Napoca) MSC: 06C05 Modular lattices, Desarguesian lattices 06B35 Continuous lattices and posets, applications 16P60 Chain conditions on annihilators and summands: Goldie-type conditions 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) 18E15 Grothendieck categories (MSC2010) Keywords:modular lattice; Goldie dimension; QFD lattice; Grothendieck category PDFBibTeX XMLCite \textit{M. Iosif}, Rev. Roum. Math. Pures Appl. 52, No. 3, 341--347 (2007; Zbl 1150.06009)