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The purity of a completion

Published online by Cambridge University Press:  18 May 2009

S. H. Cox Jr
S. H. Cox Jr
Affiliation:
University of Puerto Rico, Rio Piedras, Puerto Rico 00931
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This note establishes two statements from R. M. Fossum's review [1] of a paper by E. A. Magarian [2]. Firstly, if A → B is a pure homomorphism (of commutative rings) then A[[x1,…,xs]] → B[[x1,…, xs]] is pure. Secondly, if Rn → R is a directed family of pure homomorphisms then ∪ Rn → R is pure. A consequence is that if Rn → R is a directed family of pure homomorphisms and if R is Noetherian, then ∪ Rn[[x1,…,xs]]is Noetherian.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 127 - 129
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

1.Fossum, R. M., Review number 290, Math. Reviews 48 (1974), 58–59.Google Scholar
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