Their Quotient Of The Whole Group Ring And The Power Of Incremental Ideal Base Structure

In the study of algebra theory, integral group ring is a kind of important ring, especially its structure of n'th augmentation ideals A"(G) and their consecutivequotients Qn(G)= Δn(G)/ΔN+1(G) are central problem people concerned. In firstchapter of this thesis, we introduce concisely knowing results about the structure of n'th augmentation ideals Δn (G) and their consecutive quotients Qn( G). In chapter two and three, we select two kinds of commutative groups with special structure as object, to discuss their structure of n'th augmentation ideals Δn(G) and theirconsecutive quotients Qn(G). We obtained a recursive relation between A"(G) and Δn+l (G) and used this recursive relation as well as inductive method to get an explicit basis of Δn (G). Based on this explicit basis of Δn ( G), we have determined the structure of Qn(G).