![Example: [Z m ;+,*] is a field iff m is a prime number [a] -1 =? If GCD(a,n)=1,then there exist k and s, s.t. ak+ns=1, where k, s Example: [Z m ;+,*] is a field iff m is a prime number [a] -1 =? If GCD(a,n)=1,then there exist k and s, s.t. ak+ns=1, where k, s ](https://images.slideplayer.com/31/9708903/slides/slide_4.jpg)
Example: [Z m ;+,*] is a field iff m is a prime number [a] -1 =? If GCD(a,n)=1,then there exist k and s, s.t. ak+ns=1, where k, s
![SOLVED: Question 2 [19 marks] (a) Define what is meant by a ring homomorphism between two rings R and S, and define what is meant by its kernel: (6) Suppose that 0 SOLVED: Question 2 [19 marks] (a) Define what is meant by a ring homomorphism between two rings R and S, and define what is meant by its kernel: (6) Suppose that 0](https://cdn.numerade.com/ask_images/44065acaa9c74122a98d33e110a8359a.jpg)
SOLVED: Question 2 [19 marks] (a) Define what is meant by a ring homomorphism between two rings R and S, and define what is meant by its kernel: (6) Suppose that 0
![SOLVED: Definition: Let o: R = be a ring homomorphism between rings Then the kernel of 0 is ker(o) = re R:o(r) = 0. Proposition 2.0 If 0: R 7 5 i SOLVED: Definition: Let o: R = be a ring homomorphism between rings Then the kernel of 0 is ker(o) = re R:o(r) = 0. Proposition 2.0 If 0: R 7 5 i](https://cdn.numerade.com/ask_images/feed107dd00e4ab8aab2f799d810b79c.jpg)
SOLVED: Definition: Let o: R = be a ring homomorphism between rings Then the kernel of 0 is ker(o) = re R:o(r) = 0. Proposition 2.0 If 0: R 7 5 i
![abstract algebra - Substitution principle example? (for ring homomorphisms $R[x]\to S$) - Mathematics Stack Exchange abstract algebra - Substitution principle example? (for ring homomorphisms $R[x]\to S$) - Mathematics Stack Exchange](https://i.stack.imgur.com/hlYNb.png)
abstract algebra - Substitution principle example? (for ring homomorphisms $R[x]\to S$) - Mathematics Stack Exchange
✓ Solved: Prove that every ring homomorphism ϕ from Zn to itself has the form ϕ(x)=a x, where a^2=a.
Important theorems about ring homomorphisms and ideals. 1. Suppose that R and R' are rings and that φ : R -→ R' is a ring hom
![SOLVED: 1. Prove that if rings R and S are isomorphic, then they must have the same characteristic. Show by example that the converse fails. Let F be a field and a SOLVED: 1. Prove that if rings R and S are isomorphic, then they must have the same characteristic. Show by example that the converse fails. Let F be a field and a](https://cdn.numerade.com/ask_images/e29e9fb8afdd439fa9cf665fd825964c.jpg)