On the complete integral closure of an integral domain
- 1 August 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 6 (3) , 351-361
- https://doi.org/10.1017/s1446788700004304
Abstract
We consider in this paper only commutative rings with identity. When R is considered as a subring of S it will always be assumed that R and S have the same identity. If R is a subring of S an element s of S said to be integral over R if s is the root of a monic polynomial with coefficients in R. Following Krull [8], p. 102, we say s is almost integral over R provided all powers of s belong to a finite R-submodule of S. If R1 is the set of elements of S almost integral over R we say R1 is the complete integral closure of R in S.Keywords
This publication has 2 references indexed in Scilit:
- Some Counterexamples Related to Integral Closure in [[ x ]]Transactions of the American Mathematical Society, 1966
- Primary Ideals and Valuation IdealsTransactions of the American Mathematical Society, 1965