Yes. (Smile)StefanM said:Is this correct?
A homomorphism of rings is a map between two rings that preserves the ring structure. This means that the map must preserve addition, multiplication, and the identity elements of both rings.
While a homomorphism of rings only preserves the ring structure, an isomorphism also preserves the bijective property, meaning the map has both an inverse and a one-to-one correspondence between elements of the two rings.
Some important properties of a homomorphism of rings include: it preserves the identity element, it distributes over addition and multiplication, it preserves inverses, and it preserves the zero element.
Yes, the map f:C->Z, where C is the set of complex numbers and Z is the set of integers, is a homomorphism. It preserves addition, multiplication, and the identity elements of both C and Z.
Examples of homomorphisms of rings include the identity map, the zero map, and the inclusion map. Other examples include the map f:Z->Z, where f(n) = 2n, and the map g:R[x]->R, where g(p(x)) = p(0).