# Integral closures of ideals in the Rees ring

Colloquium Mathematicae (1993)

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

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topTiraş, 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

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