12 Pages

Almost Generalized GCD-Domains

WithL. Rebecca

GCD-domains are an important class of integral domains from classical ideal theory. They can be characterized by the property that the intersection of any two principal ideals is principal. This property can be generalized in various ways. One such generalization is called a generalized GCD-domain and the second type of generalization of a GCD-domain is called an almost GCD (AGCD)-domain. This chapter presents several equivalent conditions for an integral domain to be an almost generalized GCD (AGGCD)-domain. Since a principal ideal is invertible, it is obvious that every AGCD-domain is an AGGCD-domain. Another class of examples of AGGCD-domains are the almost Prüfer domains.