Syarat Perlu Dan Cukup Elemen Nilpoten Dalam Ring Deret Pangkat = The Necessary And Sufficient Conditions For Nilpotent Elements In Ring Of Generalized Power Series

Abstract

ABSTRACT Let S be a strictly ordered monoid and R be a ring with an identity element. In this thesis we study some properties of Artinian ordered set and Notherian ordered set of support of functions from S to R. The structure is used to construct the ring of generalized power series A = [[R51], that is more general than the formalized power series ring R[[X]]. Furthermore, in this thesis we will investigate the condition of A = [[Rsl] to be an integral domain, a primary ring. Then start learning the nilpotent elements of A=[[Rsl] , as well as determining the conditions of A =[[Rs,I] to be a reduced ring. Key words : ordered monoid, prime ideal, primary ideal, nilpotent element