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A combinatorial problem in Abelian groups

Published online by Cambridge University Press:  24 October 2008

Kenneth Rogers
Kenneth Rogers
Affiliation:
Department of Mathematics, University of California at Los Angeles
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Extract

Let α be a prime element of the ring of integers of an algebraic number field, R. Mr C. Sudler verbally raised the question as to how many prime ideal factors α can have. This is equivalent to a problem on the group of ideal classes of R, as we now show. If there is a prime α = p1p2 … Pk, where the prime ideal pi, is in the ideal class Pi, then P1P2…Pk equals the identity class, but no subproduct has this property. The converse holds since every ideal class contains prime ideals. So the problem is equivalent to one on finite Abelian groups, which we now write additively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 559 - 562
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCE

(1)Erdős, P.Ginzburg, A. and Ziv, A.Theorem in the additive number theory. Bull. Res. Council Israel, Sect. F, 10 (1961), Fl.Google Scholar