Submodules that have supplements

Abstract

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