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A note on regular local Noether lattices II

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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Let (R, M) be a local ring and let R* be the M-adic ring completion of R. It is well known that R is a regular local ring if and only if R* is a regular local ring. The purpose of the note is to show that this result is essentially a consequence of a more general theory concerning local Noether lattices which was developed in [6].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 157 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Bogart, K. P., Structure theorems for regular local Noether lattices, Michigan Math. J. 15 (1968), 167–176.Google Scholar
2.Dilworth, R. P., Abstract commutative ideal theory, Pacific J. Math. 12 (1962), 481–498.CrossRefGoogle 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
5.Johnson, E. W., A-transforms and Hilbert functions on local lattices, Trans. Amer. Math. Soc. 137 (1969), 125–139.Google Scholar
6.Johnson, J. A., A note on regular local Noether lattices, Glasgow Math. J. 15 (1974), 159–161.Google Scholar
7.Nagata, M., Local Rings (Interscience, 1962).Google Scholar
8.Northcott, D. G., Ideal Theory (Cambridge, 1963).Google Scholar