These are precisely the ring homomorphisms which are continuous with respect to the given topologies on " R " and " S ".
32.
But this map is not a ring homomorphism : the right-evaluation of a product differs in general from the product of the right-evaluations.
33.
Then there is a surjective ring homomorphism from W ( " K " ) to this obtained by mapping a class to discriminant and rank mod 2.
34.
Any ring homomorphism " R " ?! " S " induces; in fact, any ring homomorphism between matrix rings arises in this way.
35.
Any ring homomorphism " R " ?! " S " induces; in fact, any ring homomorphism between matrix rings arises in this way.
36.
Many authors do not require rings to have a multiplicative identity element and, accordingly, do not require ring homomorphism to preserve the identity ( should it exist ).
37.
When the algebraic structure is a ideals for kernels of ring homomorphisms ( in the case of non-commutative rings, the kernels are the two-sided ideals ).
38.
One can check that is a functor from the category of rings to the category of groups : every ring homomorphism induces a group homomorphism, since maps units to units.
39.
When " X " is smooth over " k ", this homomorphism can be identified with a ring homomorphism from the Chow ring to etale cohomology.
40.
Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms.
