# Ring extension

Ring extension

In mathematics, more specifically in ring theory, a ring extension or extension ring is a ring "R" with a subring "S". We write "R"/"S" and say "R" is a "ring extension" of "S"

Given an extension "R"/"S" of commutative rings and a prime ideal P of "R", it follows thatthe intersection, say p, of P with "S" is a prime ideal of "S". In this case we say that P lies over p. The situation is more complicated when "R" is not commutative.

Examples

* A field extension is a special case of ring extension.

* Integral extension
* Group extension
* Algebraic extension
* Ore extension

References

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