Submodules That Have Supplements

Abstract

In this thesis we study theK -elements of extension modules where R is a principal ideal domain. In general K -elements need not form a submodule in an extension module but if C is divisible and almost all primary components of C are zero, they coincide with torsion elements of extension module. If C is divisible and torsion, not all primary components of C are zero, andAis torsion free ok rank 1 then a nonzero element of extension module is a K-element if and only if the type of the element in extension module is less than or equal to the type of A. Also we define B-elements which form a submodule of extension module and study their relation with K-elements.