• Patching together a minimal overring, Vol 36, No.4

Authors: David E. Dobbs, Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300 (dobbs@math.utk.edu) and Jay Shapiro, Department of Mathematics, George Mason University, Fairfax, Virginia 22030-4444 (jshapiro@gmu.edu).
Patching together a minimal overring, pp. 985-995.
ABSTRACT. Let R be a (commutative integral) domain and M a maximal ideal of R. Let T(M) be a minimal ring extension of RM. Our basic question is (*): does there exist a (necessarily minimal) ring extension T of R such that TM is isomorphic to T(M) and TN = RN canonically for each prime ideal N of R that is distinct from M? The answer to (*) is affirmative if T(M) is not a domain. Several equivalences are given for an affirmative answer to (*) when T(M) is a domain, such as the existence of a in T(M) \ RM such that M is the radical of (R:_Ra). If R is a Prüfer domain that has property (#), the answer to (*) is affirmative for all such data {M, T(M)}; the converse is false in general but holds for Prüfer domains each of whose maximal ideals is branched.

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Patching together a minimal overring, Vol 36, No.4

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