Generalized Hill lemma, Kaplansky theorem for cotorsion pairs and some applications

Abstract

We develop infinite dimensional Jordan-Hoelder theory by generalizing Hill Lemma to obtain a large family of C-filtered submodules from a single C-filtration. We use this theory to extend Kaplansky Theorem for projective modules to cotorsion pairs, and to prove a structure theorem for strongly flat modules over valuation domains.

Keywords

• Generalized
• lemma
• Kaplansky
• theorem
• cotorsion
• pairs
• applications