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 that the 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.

See also

• Integral extension
• Group extension
• Algebraic extension
• Ore extension

References

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2008)

This algebra-related article is a stub. You can help Wikipedia by expanding it.