Abstract: 

A module is uniserial if its lattice of submodules is linearly ordered under inclusion and is serial if it is a direct sum of uniserial modules. A module over a ring R is said to satisfy the serial embedding property (SEP) if it is (isomorphic to) a submodule of a serial R-module, or equivalently, if it can be embedded in a serial R-module. In this talk, we present a result that an integral domain D (not a field) is Dedekind if and only if torsion D-modules satisfy the SEP.

This is a joint work with my thesis advisors Dr. Miodrag Iovanov and Dr. Victor Camillo.