الملخص الإنجليزي
Projective and flat modules are two important classes of modules heavily used in commutative algebra, homological algebra, and in many other areas of mathematics. Multiplication modules have been introduced and studied only recently. The aim of this project is to study the three classes of modules mentioned above and explore the connections between them. In the first chapter, we give a review of the basic properties of modules over commutative rings, which will be needed in the following chapters. In chapter two we give some characterizations of multiplication modules and study their stability under direct sums, intersections, tensor products and so on. In the same chapter we give some relations between multiplication modules and Artinian modules (resp. week cancellation modules). In general, projective modules are introduced before flat modules but in our case we do the opposite, we start first with flat modules, and then we restrict our study to projective modules. Following that philosophy, in chapter three, we introduce flat modules and give some of their properties and characterizations. In chapter four, we consider projective modules; we give some of their properties and characterizations. In the last chapter, we explore the connections between multiplication, projective and flat modules.
