Integral closures of ideals in the Rees ring

Y. Tiraş

Colloquium Mathematicae (1993)

  • Volume: 64, Issue: 2, page 185-191
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Tiraş, Y.. "Integral closures of ideals in the Rees ring." Colloquium Mathematicae 64.2 (1993): 185-191. <http://eudml.org/doc/210183>.

@article{Tiraş1993,
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.},
author = {Tiraş, Y.},
journal = {Colloquium Mathematicae},
keywords = {integral closures of ideals; Noetherian ring; Rees ring},
language = {eng},
number = {2},
pages = {185-191},
title = {Integral closures of ideals in the Rees ring},
url = {http://eudml.org/doc/210183},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Tiraş, Y.
TI - Integral closures of ideals in the Rees ring
JO - Colloquium Mathematicae
PY - 1993
VL - 64
IS - 2
SP - 185
EP - 191
AB - 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.
LA - eng
KW - integral closures of ideals; Noetherian ring; Rees ring
UR - http://eudml.org/doc/210183
ER -

References

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  1. [1] N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, Mass., 1972. 
  2. [2] H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1980. Zbl0441.13001
  3. [3] D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, 1968. Zbl0159.33001
  4. [4] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145-158. Zbl0057.02601
  5. [5] D. Rees, The grade of an ideal or module, ibid. 53 (1957), 28-42. Zbl0079.26602
  6. [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. Zbl0408.13009
  7. [7] R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press, 1990. Zbl0703.13001
  8. [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. Zbl0733.13001

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