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.
Table of Contents
- Definition: Ring of Integers
Thank you to the contributors under CC BY-SA 4.0!
- Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück