The Transfer of some Algebraic Properties from Rings and Modules into Their Extentions

Abstract

It was shown by Galovich that if R is a commutative unique factorization ring (UFR) with identity, then R is a local ring with a nil maximal ideal. In this thesis, we generalize Galovich's results to the non-commutative case. Also, we generalize Chon's results to the non-commutative case , we show that if R satisfies ACC on principal right (left) ideals, then R is atomic. Moreover, we study UFR by using lattice structure.