ArticleOriginal scientific text

Title

Integral closures of ideals in the Rees ring

Authors 1

Affiliations

  1. Hacettepe University, Department of Pure Mathematics, Beytepe Campus, 06532 Ankara, Turkey

Abstract

The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.

Bibliography

  1. N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, Mass., 1972.
  2. H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1980.
  3. D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, 1968.
  4. D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145-158.
  5. D. Rees, The grade of an ideal or module, ibid. 53 (1957), 28-42.
  6. D. Rees and R. Y. Sharp, On a theorem of B. Teissier on multiplicities of ideals in local rings, J. London Math. Soc. (2) 18 (1978), 449-463.
  7. R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press, 1990.
  8. R. Y. Sharp, Y. Tiraş and M. Yassi, Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings, J. London Math. Soc. (2) 42 (1990), 385-392.
Pages:
185-191
Main language of publication
English
Received
1991-08-30
Published
1993
Exact and natural sciences