Vélez, José A.

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Some divisibility properties in rings of polynomials over a unique factorization domain
(2005) Vélez, José A.; Cáceres, Luis F.; College of Arts and Sciences - Sciences; Castellini, Gabriele; Walker-Ramos, Uroyoán; Department of Mathematics; Rivera, Wilson
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 of the polynomial. 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.