Integral closure: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Richard Pinch
(New entry, just a stub)
(No difference)

Revision as of 13:35, 1 January 2009

In ring theory, the integral closure of a commutative unital ring R in an algebra S over R is the subset of S consisting of all elements of S integral over R: that is, all elements of S satisfying a monic polynomial with coefficients in R. The integral closure is a subring of S.

An example of integral closure is the ring of integers or maximal order in an algebraic number field K, which may be defined as the integral closure of Z in K.

References

  • Pierre Samuel (1972). Algebraic number theory. Hermann/Kershaw.