Abstract
ABSTRACT In this article, we raise the question as to what conditions permit a simple overring of a domain R —that is, a domain of the form for some f, g ∈ R such that g ≠ 0—to inherit the ascending chain condition on principal ideals from R . Our main theorem reveals that, if g is a prime element of R , the complete answer can be found by considering the Archimedean property. We then, in turn, use this theorem to establish equivalent conditions for a certain class of simple overring to inherit the property of being a unique factorization domain from R .
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