Some Divisibility Properties in Ring of Polynomials over a Unique Factorization Domain

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Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is possible to prove that under certain conditions, the domain of coefficients must have infinitely many prime elements. We give alternative characterizations for D-rings and present various examples.
16 pages

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Commutative Algebra, 13A05

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http://salesiana.dossiersoluciones.com/handle/123456789/162523

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.1398
 http://arxiv.org/abs/0806.1398

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arXiv