On Noetherian Rings

Abstract: In this thesis we study a special class of rings called Noetherian rings. Theserings satisfy certain finite conditions on their ideals and appear in manydifferent fields of algebra. With an emphasis on commutative Noetherianrings we examine their structure and properties, their relation to anotherspecial class of rings called Artinian rings and the practicality of workingwith Noetherian rings in algebraic geometry. Some central results whichare proved is the Lasker-Noether Theorem, that Noetherian rings have anilpotent nilradical and that Artinian rings are Noetherian.