Some Properties of Completely Arithmetical Rings  

作　　者：Xinmin Lu 

机构地区：[1]School of Science, Nanjing University of Science and Technology Nanjing 210093, Ghina

出　　处：《Algebra Colloquium》2016年第1期83-88,共6页代数集刊（英文版）

摘　　要：In this paper, we introduce the concept of completely arithmetical rings and investigate their properties. In particular, we prove that if R is a completely arithmetical ring with J（R） =0, then Ko（R） ≌Z^n for some positive integer n. We also show that such a ring is precisely a ring in which every proper ideal can be written uniquely as a product of finitely many distinct completely strongly irreducible ideals.In this paper, we introduce the concept of completely arithmetical rings and investigate their properties. In particular, we prove that if R is a completely arithmetical ring with J（R） =0, then Ko（R） ≌Z^n for some positive integer n. We also show that such a ring is precisely a ring in which every proper ideal can be written uniquely as a product of finitely many distinct completely strongly irreducible ideals.

关 键 词：completely arithmetical ring completely irreducible ideal completely stronglyirreducible ideal K0-group 

分 类 号：O121[理学—数学] O177.1[理学—基础数学]