Ring-theoretic properties of locally Mori domains and rings of the form \(\text{Int}(E, D)\). (English) Zbl 1541.18004
Summary: An integral domain \(D\) is said to be locally Mori if any localization of \(D\) at a maximal ideal is a Mori domain. In this paper we are concerned with some ring-theoretic properties of locally Mori domains and their rings of integer-valued polynomials. First, we present some results on the transfer of the locally Mori property to flat overrings, Nagata ideal transforms, polynomial ring extensions and pullback constructions. Then, we investigate rings of integer-valued polynomials over (locally) Mori domains, and for an integral domain \(D\), we give a necessary condition for \(\text{Int}(D)\) to be an MZ-Mori domain.
MSC:
| 18A30 | Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) |
| 13B30 | Rings of fractions and localization for commutative rings |
| 13C11 | Injective and flat modules and ideals in commutative rings |
| 13F05 | Dedekind, Prüfer, Krull and Mori rings and their generalizations |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
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