45 research outputs found

    Semilocal Generic Formal Fibers

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    Let T be a complete local ring and C a finite set of incomparable prime ideals of T. We find necessary and sufficient conditions for T to be the completion of an integral domain whose generic formal fiber is semilocal with maximal ideals the elements of C. In addition, if char T = 0, we give necessary and sufficient conditions for T to be the completion of an excellent integral domain whose generic formal fiber is semilocal with maximal ideals the elements of C.Comment: 15 page

    Characterization of completions of excellent domains of characteristic zero

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    AbstractWe show that a complete local ring T containing the integers is the completion of a local excellent integral domain if and only if it is reduced, equidimensional, and no integer of T is a zero divisor

    Gluing Associated Prime Ideals of Small Height

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    Let BB be a local (Noetherian) ring and suppose that BB has nn associated prime ideals where nβ‰₯2n \geq 2. We identify sufficient conditions for there to exist a local (Noetherian) subring SS of BB such that SS and BB have the same completion and SS has exactly nβˆ’1n - 1 associated prime ideals. We include applications and consequences of this result.Comment: 14 page
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