Integral closures of ideals in the Rees ring

• Autorzy: Y. Tiraş
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 64
• Numer: 2
• Strony: 185-191

Daty

wydano

1993

otrzymano

1991-08-30

Twórcy

autor

Y. Tiraş

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

Bibliografia

• [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.