| The notion of pure subgroups was first introduced by Prufer in 1923. A subgroup G of a group A is said to be pure in A if the equation nx = g, where n ∈ Z and g ∈ G, is solvable in G whenever it is solvable in A. The notion of purity was extended to submodules by several authors (e.g. Cohn, Fuchs, and Walker), and has since become an extensively studied topic in module theory. In 1967, B. H. Maddox introduced absolutely pure modules. This notion was studied and developed by other authors, for example C. Megibben and B. Stenstrom. In this thesis we will present various properties of absolute purity, as well as some ring characterizations that use this notion. A generalization of absolute purity, due to Lee, will also be discussed. |
