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A note on regular local Noether lattices

Published online by Cambridge University Press:  18 May 2009

Johnny A. Johnson
Johnny A. Johnson
Affiliation:
University of Houston, Department of Mathematics, Houston, Texas 77004, U.S.A.
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If R is a local (Noetherian) ring, it is well known that R is regular if and only if its completion is regular. It is the purpose of this note to show that a similar result is true for Noether lattices.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 2 , September 1974 , pp. 159 - 161
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Dilworth, R. P., Abstract commutative ideal theory, Pacific J. Math. 12 (1962), 481–498.CrossRefGoogle Scholar
2.Johnson, E. W., A-transforms and Hilbert functions on local lattices, Trans. Amer. Math. Soc. 137 (1969), 125–139.Google Scholar
3.Johnson, E. W. and Johnson, J. A., M-primary elements of a local Noether lattice, Canad. J. Math. 22 (1970), 327–331.CrossRefGoogle Scholar
4.Johnson, E. W. and Johnson, J. A., M-primary elements of a local Noether lattice, Corrigendum, Canad. J. Math. 25 (1973), 448.CrossRefGoogle Scholar