Definition: Integral Element

Let \(S\) be an algebra over the ring \(R\). An element \(x\in S\) is called integral over \(R\), if there is a monic polynomial \(p\in R[X]\) with \(p\neq 0\) and \(p(x)=0\), i.e. \(x\) is a root of the monic polynomial.

  1. Definition: Ring of Integers

Definitions: 1


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References

Bibliography

  1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition

Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück