ring homomorphism

Every ideal is the kernel of a ring homomorphism and vice versa.

The composition of two ring homomorphisms is a ring homomorphism.

In fact it is a ring homomorphism.

This shows that "F" is a ring homomorphism.

In other words, f is a (graded) ring homomorphism.

A field automorphism is a bijective ring homomorphism from a field to itself.

To see this, just choose a ring homomorphism between the underlying rings that does not change the ring action.

A ring homomorphism is a homomorphism between two rings.

Conversely, if A is an algebra over R, then is such a ring homomorphism.

For this purpose, one abstractly defines a field extension as an injective function ring homomorphism between two fields.

A bijective ring homomorphism is called a ring isomorphism.

A ring homomorphism whose domain is the same as its range is called a ring endomorphism.

For rings with identity, the kernel of a ring homomorphism is a subring without identity.

A ring homomorphism that is injective is a ring monomorphism.

Wiles had the insight that in many cases this ring homomorphism could be a ring isomorphism.

Let be a ring homomorphism.

The preimage of a prime ideal under a ring homomorphism is a prime ideal.

This inclusion thus also is an example of a ring homomorphism which is both mono and epi, but not iso.

If f is bijective, then its inverse f is also a ring homomorphism.

There is a natural ring homomorphism , the Chern character, such that is an isomorphism.

Wiles denotes this matching (or mapping) that, more specifically, is a ring homomorphism:

A genus is a ring homomorphism from a bordism ring into another ring.

The ring homomorphism induces maps in K-theory .

In the special case where a ring homomorphism f is a bijection, then f is called an isomorphism.

In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication.