Inductive Rings and Systems of Diophantine Equations  

作　　者：Rong Fang BIE Shi Qiang WANG 

机构地区：[1]College of Information Science, Beijing Normal University, Beijing 100875, P. R. China [2]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2006年第5期1549-1556,共8页数学学报（英文版）

基　　金：Supported by NNSF(No. 19931020, No. 10001006 and No. 60273015)of China

摘　　要：In this paper, by using model-theoretic methods, it is shown that some systems of unsolved cubic diophantine equations in number theory can have solutions in certain inductive extension rings of the ring I of rational integers. These inductive rings are not fields, and every element of them is a sum of 4 cubes and a sum of 3 squares. Also some of them satisfy the Goldbach conjecture and some others don＇t.In this paper, by using model-theoretic methods, it is shown that some systems of unsolved cubic diophantine equations in number theory can have solutions in certain inductive extension rings of the ring I of rational integers. These inductive rings are not fields, and every element of them is a sum of 4 cubes and a sum of 3 squares. Also some of them satisfy the Goldbach conjecture and some others don＇t.

关 键 词：Inductive rings Systems of unsolved cubic diophantine equations Model theory 

分 类 号：O156.7[理学—数学]