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Fractional powers of a submodule of an algebra

Part of: Theory of modules and ideals

Published online by Cambridge University Press:  26 February 2010

D. Kirby  and
H. A. Mehran
D. Kirby
Affiliation:
The University, Southampton.
H. A. Mehran
Affiliation:
The University, Southampton.
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Extract

Let R be a commutative ring with identity, and let U be a unitary commutative R-algebra with identity. In [1] Gilmer defines the (l/n)th power (n a positive integer) of a valuation ideal R when R is a domain. Sections 2, 3 of the present note are devoted to the study of an extension of this notion to positive rational powers of an arbitrary R-submodule of U.

MSC classification

Secondary: 13C99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 18 , Issue 1 , June 1971 , pp. 8 - 13
Copyright
Copyright © University College London 1971

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References

1.Gilmer, R. W., “A class of domains in which primary ideals are valuation ideals,” Math. Ann., 161 (1965), 247–254.CrossRefGoogle Scholar
2.Kirby, D., “Integral dependence and valuation algebras”, Proc. London Math. Soc., (3), 20 (1970), 79–100.CrossRefGoogle Scholar
3.Kirby, D. and Mehran, H. E., “Homomorphisms and the space of valuation modules,”, Quart. J. Math. (Oxford), (2), 21 (1970), 439–443.CrossRefGoogle Scholar
4.Nagata, M., Local rings (Interscience, 1962).Google Scholar
5.Zariski, O. and Samuel, P., Commutative Algebra, Vol. II (Van Nostrand, 1960).CrossRefGoogle Scholar