Integral element

In the mathematical subfield of commutative algebra wholeness is a slight modification of the notion of an algebraic element, but causes significantly different properties.

Definition

There was a ring and a - algebra. Then is called an element all over, if there is a monic polynomial

Are such that

Applies.

Is, over all, if every element of is all about. If, in particular, one speaks of a whole ring expansion.

For an arbitrary algebra is called the quantity of all elements of the whole concluding in.

Properties

• The whole concluding in is a subalgebra of.

• A -algebra if and only finally, when they finally produced and is quite.

Examples

• If and so is the whole conclusion of in the same

• See wholeness ring

• Commutative Algebra