بررسی تجزیه اعداد تام درجه دوم

Abstract

In this paper,  domains are examined. These domains often have no unique factorization property and are therefore a good example of problems that have historically played a pivotal role in the emergence of the concept of ideal. First, a brief history of the subject is given, then the domains show how the concept of an ideal can be used to "restore" the unique factorization of some domains that lack this property. Also, the unique generalization of the factorization of an ideal by the product of the prime ideals in the Kummer domains without sequence of factors is discussed.