Commutative Algebra

pp 331-351


Integral Closure

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Since 2006, when the book on integral closures with Huneke and Swanson (Integral Closure of Ideals, Rings, and Modules. Cambridge University Press, Cambridge, 2006) was published, there has been more development in the area. This chapter is an attempt at catching up with that development as well as to fill in a few omissions. Some topics are worked out in detail whereas others are only outlined or mentioned.


Integral closure Rees valuations Computing integral closure Lipman–Sathaye theorem Multiplicity j-multiplicity Epsilon multiplicity Monomial ideals Goto numbers

Subject Classifications:

13B22 Secondary: 13P05, 13P25, 13H15