The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Local Nullstellensatz over Commutative Ground Rings


Affiliations
1 Department of Mathematics, Missouri State University, Springfield, Missouri 65897, United States
2 Department of Mathematics, University of California, Riverside, California 92521-0135, United States
     

   Subscribe/Renew Journal


It is shown that a local Nullstellensatz holds over an arbitrary commutative ring A (with identity 1 ≠ 0); specifically, if B = A[x1, . . . , xn] is a finitely generated extension ring of A and N is a maximal ideal in B, then NBN = (N ∩ A, x1 − c1, . . . , xn − cn)BN for some c1, . . . , cn ∈ BN .


Keywords

G-Ideal, Nullstellensatz, Maximal Ideal, Polynomial Ring.
Subscription Login to verify subscription
User
Notifications
Font Size


  • D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York, 1995.

  • I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, 1970.

  • P. Kemp, L. J. Ratliff, Jr., and K. Shah, Depth one homogeneous prime ideals in polynomial rings over a field, Journal of Indian Math. Soc. (accepted).

  • M. Nagata, Local Rings, Interscience, John Wiley, New York, 1962.

  • O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, D. Van Nostrand, New York, 1958.

  • O. Zariski and P. Samuel, Commutative Algebra, Vol. 2, D. Van Nostrand, New York, 1960.


Abstract Views: 185

PDF Views: 0




  • Local Nullstellensatz over Commutative Ground Rings

Abstract Views: 185  |  PDF Views: 0

Authors

Paula Kemp
Department of Mathematics, Missouri State University, Springfield, Missouri 65897, United States
Louis J. Ratliff
Department of Mathematics, University of California, Riverside, California 92521-0135, United States
Kishor Shah
Department of Mathematics, Missouri State University, Springfield, Missouri 65897, United States

Abstract


It is shown that a local Nullstellensatz holds over an arbitrary commutative ring A (with identity 1 ≠ 0); specifically, if B = A[x1, . . . , xn] is a finitely generated extension ring of A and N is a maximal ideal in B, then NBN = (N ∩ A, x1 − c1, . . . , xn − cn)BN for some c1, . . . , cn ∈ BN .


Keywords


G-Ideal, Nullstellensatz, Maximal Ideal, Polynomial Ring.

References