Representations of relatively complemented modular lattices
Bjàrni Jónsson · Transactions of the American Mathematical Society · 1962
Introduction.A module over a ring will be said to be locally projective if and only if every finitely generated submodule is projective.As will be shown (7.14), it readily follows from known facts that if M is a locally projective module over a regular ring R, then the set L(M, R) of all finitely generated submodules of M is a relatively complemented modular lattice.This paper is concerned with the representation problem suggested by the above observation.The fundamental theorem, 8.2, gives sufficient conditions in order for a relatively complemented modular lattice B to be isomorphic to L(M, R) for some locally projective module Mover a regular ring R. Essential use will be made of the results in Jónsson [7], and henceforth that paper will be referred to briefly as CM.In particular, the embedding theorem CM3.2