![abstract algebra - Proving that a ring homomorphism $R[X] \to R^R, p \mapsto \underline p$ takes $1$ to $1$ - Mathematics Stack Exchange abstract algebra - Proving that a ring homomorphism $R[X] \to R^R, p \mapsto \underline p$ takes $1$ to $1$ - Mathematics Stack Exchange](https://i.stack.imgur.com/fToEf.png)
abstract algebra - Proving that a ring homomorphism $R[X] \to R^R, p \mapsto \underline p$ takes $1$ to $1$ - Mathematics Stack Exchange
✓ Solved: Suppose that ϕ: R → S is a ring homomorphism and that the image of ϕ is not {0} . If R has...
![abstract algebra - Does a ring homomorphism necessarily induce a map of their spectrums? - Mathematics Stack Exchange abstract algebra - Does a ring homomorphism necessarily induce a map of their spectrums? - Mathematics Stack Exchange](https://i.stack.imgur.com/Rfy7U.png)
abstract algebra - Does a ring homomorphism necessarily induce a map of their spectrums? - Mathematics Stack Exchange
![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
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: Prove that every ring homomorphism ϕ from Zn to itself has the form ϕ(x)=a x, where a^2=a.
![abstract algebra - For a ring homomorphism, $\phi\left ( x \right )=0$ or $\phi\left ( x \right )=x.$ - Mathematics Stack Exchange abstract algebra - For a ring homomorphism, $\phi\left ( x \right )=0$ or $\phi\left ( x \right )=x.$ - Mathematics Stack Exchange](https://i.stack.imgur.com/3WkaN.png)
abstract algebra - For a ring homomorphism, $\phi\left ( x \right )=0$ or $\phi\left ( x \right )=x.$ - Mathematics Stack Exchange
![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)
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
![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)