Some Diophantine equations associated to seminormal Cohen-Kaplansky domainsReport as inadecuate




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* Corresponding author 1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Abstract : 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.

Keywords : CK domain Half-factorial Seminormal T-closed Diophantine equations





Author: Abdallah Badra - Martine Picavet-L-Hermitte -

Source: https://hal.archives-ouvertes.fr/



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