Prime submodules and Dedekind rings

Prime submodule which is a version of prime ideal is an important concept formodules defined on commutative rings. By making use of Çallıalp and Tekir?s (2009)book, Dummit and Foote?s (1999) book, Kaplansky?s (1952) book and Jenkins andSmith?s (1992) article for this concept in this thesis, we determine height of primesubmodule chain and determine rings by using it.This thesis consists of four chapters. In the .rst chapter, we give some basicdefinitons and notation used throughout thesis. In the second chapter, we give somebasic definitons and results which will be used in the later chapters. In the thirdchapter, we give some definitions, theorems and results related with the moduletheory, which are essential for developing the aim of this thesis.Fourth chapter is started by minimum prime submodules. Subsequent to it,concept of a module dimension and ring are introduced and their basic characteristicsare given. In the remainder of this chapter, how dimension of module ties in ring onwhich module depends is examined. By using these, a characterizatin is given forDedekind ring.KEYWORDS: Prime Submodule, Radical formula Dedekind Ring, Dimension of a Module