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

Weisstein, Eric W., "Extension Ring" from MathWorld.