TY - JOUR

T1 - Semi-local formal fibers of minimal prime ideals of excellent reduced local rings

AU - Arnosti, N.

AU - Karpman, R.

AU - Leverson, C.

AU - Levinson, J.

AU - Loepp, S.

PY - 2012

Y1 - 2012

N2 - Let T be a complete local (Noetherian) ring containing the rationals, and let C be a finite set of incomparable non-maximal prime ideals of T partitioned into m subsets C1,... , Cm. We find necessary and sufficient conditions for T to be the completion of an excellent reduced local ring A with precisely m minimal prime ideals J1,.. . , Jm such that, for each i = 1, 2,... , m, the maximal elements of the set {Q ε SpecT | Q ∩ A = Ji} are precisely the elements of Ci. We also find necessary and sufficient conditions for T to be the completion of such a ring A for the case where A need not be excellent.

AB - Let T be a complete local (Noetherian) ring containing the rationals, and let C be a finite set of incomparable non-maximal prime ideals of T partitioned into m subsets C1,... , Cm. We find necessary and sufficient conditions for T to be the completion of an excellent reduced local ring A with precisely m minimal prime ideals J1,.. . , Jm such that, for each i = 1, 2,... , m, the maximal elements of the set {Q ε SpecT | Q ∩ A = Ji} are precisely the elements of Ci. We also find necessary and sufficient conditions for T to be the completion of such a ring A for the case where A need not be excellent.

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U2 - 10.1216/JCA-2012-4-1-29

DO - 10.1216/JCA-2012-4-1-29

M3 - Article

AN - SCOPUS:84872842569

SN - 1939-0807

VL - 4

SP - 29

EP - 56

JO - Journal of Commutative Algebra

JF - Journal of Commutative Algebra

IS - 1

ER -