Derong Qiu
Published 2009-12-22, updated 2012-06-03Version 3
In this paper, by introducing and constructing several new structures about the decomposition phenomenon in algebra, we study the sum-factor collapse property of an arbitrary ring. As an application, we study and analyze several classical problems in additive number theory by this new algebraic and combinatory method. Some further questions are also presented and discussed.
Comments: 36 pages; The abstract is slightly changed; the original Remark 3.18 is omitted; the original Theorem 3.16 is written now as Theorem 3.15, and a few new results are added into the present Theorem 3.16, the new Remark 3.17 is added to give some explanation of applications
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Counterexample to a Conjecture of Dombi in Additive Number Theory
A general formula in Additive Number Theory
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