Unit Group Of Residue Class Ring Of Integers Modulo N

Unit group is one of the basic and important concepts in algebra. More and more scholars have investigated the unit groups of rings, especially those on matrix rings, group rings, residue class rings of integers modulo n, Gaussian integral rings, and so on. There have been a lot of research papers on unit groups appearing in the literature. By using the Chinese remainder theorem and decomposition theorem for the structures of the residue class rings mod n and its unit groups, we consider the structure of()nU ? and fully determined all the precise values of n, when the order of()nU ? was given to be 2pqr,2p qr,2p q r,2p q r? ? ? ? ? ?,where p,q,r are prime numbers(not necessarily distinct), and ?,? and ? are positive integers.The thesis is arranged as follows:Chapter 1 is the Introduction part.Chapter 2 gives some related concepts, properties and results of the residue class rings of integers mod n.Chapter 3 determines all the precise values of n for the structure of()nU ? in the case that the order of()nU ? is2 pqr.Chapter 4 determines all the precise values of n for the structure of()nU ? in the case that the order of()nU ? is 2p?qr,2p?q?r,2p?q?r? respectively.Chapter 5 is the Summary part.