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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

  1. Definition: Integral Element
  2. Definition: Integral Closure

Mentioned in:

Definitions: 1 2 3 4 5

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References

Adapted from CC BY-SA 3.0 Sources:

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