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Article Dans Une Revue International Journal of Mathematics, Game Theory and Algebra Année : 2006

Some Diophantine equations associated to seminormal Cohen-Kaplansky domains

Résumé

A Cohen-Kaplansky domain (CK domain) R is an integral domain where every nonzero nonunit element of R is a ¯nite product of irreducible elements and such that R has only ¯nitely many nonassociate irreducible elements. In this paper, we investigate seminormal CK domains and obtain the form of their irreducible elements. The solutions of a system of diophantine equations allow us to give a formula for the number of distinct factorizations of a nonzero nonunit element of R, with an asymptotic formula for this number.
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Dates et versions

hal-00477416 , version 1 (06-05-2010)

Identifiants

  • HAL Id : hal-00477416 , version 1

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Abdallah Badra, Martine Picavet-L'Hermitte. Some Diophantine equations associated to seminormal Cohen-Kaplansky domains. International Journal of Mathematics, Game Theory and Algebra, 2006, 15 (2), pp.139-153. ⟨hal-00477416⟩
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