The Impact of Dilworth’s Work on Semimodular Lattices on the Kurosch-Ore Theorem
Manfred Stern · Birkhäuser Boston eBooks · 1990
In his papers on decompositions in lattices, Dilworth clarifies, among other things, the scope of the celebrated Kurosch-Ore Theorem. In particular, he shows that an upper semimodular lattice of finite length has the Kurosch-Ore replacement property (KORP) for meet-decompositions if and only if it is locally modular. This result and some deep generalizations are described in B. Jónsson’s article in this chapter. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.