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Definition: Algebra over a Ring
Let \((R, +,\cdot)\) and \((S,\ast,\circ)\) be commutative rings and let \(f:R\rightarrow S\) be a fixed ring homomorphism. Then \(S\) is called an \(R\)-algebra or an algebra over the ring \(R\).
Table of Contents
- Definition: Integral Element
- Definition: Integral Closure
Definitions: 1 2 3 4 5
Thank you to the contributors under CC BY-SA 4.0!
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück