In this article, we introduce and study the notion of λ-finitely embedded modules (a O-finitely embedded module is just a finitely embedded module). We extend some of the basic results of f.e. modules to λ-f.e. modules. We use this concept to give a new proof of a known result which essentially says that a module M has Krull dimension α if and only if each factor module of M is λ-f.e. for some λ≤α and α is the least ordinal with this property. It is observed that a semiprime ring R has Krull dimension λ if and only if R is λ-f.e. We improve the theorem of Matlis-Papp and some of its consequences.Finally, some known results in the literature are restated in terms of the above notion.