ring homomorphism in a sentence

Examples

1. The universal property means that any ring homomorphism from k \ langle t _ 1, \ dots, t _ m \ rangle to a matrix ring factors through F _ n.
2. The integers form a unital ring which is the most basic one, in the following sense : for any unital ring, there is a unique ring homomorphism from the integers into this ring.
3. Given a ring homomorphism f : R \ to S, the set of all elements mapped to 0 by " f " is called the kernel of " f ".
4. 16 ) " Ring morphism " Notice that the article that it links to is in fact " ring homomorphism . " That is more standard terminology, especially for an elementary / generalist approach.
5. An isomorphism is simply a bijective homomorphism . ( The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator ).
6. A ring homomorphism is said to be an "'isomorphism "'if there exists an inverse homomorphism to " f " ( i . e ., a ring homomorphism which is an inverse function ).
7. A ring homomorphism is said to be an "'isomorphism "'if there exists an inverse homomorphism to " f " ( i . e ., a ring homomorphism which is an inverse function ).
8. If R is a commutative ring and S is any localization S ^ {-1 } R can still be constructed, but the ring homomorphism from R to S ^ {-1 } R might fail to be injective.
9. Then there is a surjective ring homomorphism from W ( " K " ) to Sym ( " K " ) obtained by mapping a class to discriminant, rank mod 2, and the sequence of Hasse invariants.
10. The requirements of ring homomorphisms are such that there can be only one homomorphism from the ring of integers to any ring; in the language of category theory, "'Z "'is an initial object of the category of rings.