| Inductive Rings and Systems of Diophantine Equations |
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| 引用本文： | Rong Fang BIE Shi Qiang WANG. Inductive Rings and Systems of Diophantine Equations[J]. 数学学报(英文版), 2006, 22(5): 1549-1556. DOI: 10.1007/s10114-005-0834-8 |
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| 作者姓名： | Rong Fang BIE Shi Qiang WANG |
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| 作者单位： | [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 |
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| 基金项目： | Supported by NNSF （No. 19931020, No. 10001006 and No. 60273015） of China. |
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| 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.
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| 关 键 词： | 感应环 丢番图方方程 模型理论 有理数 |
| 收稿时间： | 2004-09-20 |
| 修稿时间： | 2004-09-202005-02-01 |
Inductive Rings and Systems of Diophantine Equations |
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| Rong Fang Bie,Shi Qiang Wang. Inductive Rings and Systems of Diophantine Equations[J]. Acta Mathematica Sinica(English Series), 2006, 22(5): 1549-1556. DOI: 10.1007/s10114-005-0834-8 |
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| Authors: | Rong Fang Bie Shi Qiang Wang |
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| Affiliation: | (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 |
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| Abstract: | 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. Supported by NNSF (No. 19931020, No. 10001006 and No. 60273015) of China |
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| Keywords: | Inductive rings Systems of unsolved cubic diophantine equations Model theory |
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