Tagged Questions
1
vote
3answers
79 views
Ring homomorphism question.
If $R$ is a ring, show that there is exactly one ring homomorphism $\phi: \mathbb{Z} \to R$.
I can't grasp the idea that there can be only one ring homomorphism. Aren't there many (at least more than ...
-1
votes
1answer
72 views
Problem of monomorphism of rings [duplicate]
Let $A$ a ring, for each monomorphism $f:A^m \rightarrow A^n$, I don't know how to prove that $m\leq n$. I can't start the problem, I have no idea, help me please.
4
votes
5answers
246 views
In a ring homomorphism we always have $f(1)=1$? [duplicate]
Possible Duplicate:
the image of $1$ by a homomorphism between unitary rings
I'm studying the Atiyah's commutative algebra book and I realized that in the beginning of the book, the author ...
1
vote
3answers
86 views
Are monomorphisms of rings injective?
Let $R$ and $S$ be rings and $f:R\to S$ a monomorphism. Is $f$ injective?
3
votes
1answer
211 views
the image of $1$ by a homomorphism between unitary rings
let $R$ and $S$ be unitary rings and $\phi:R\rightarrow S$ a ring homomorphism.
is the following correct:
$\phi(1_R\cdot1_R)=\phi(1_R)\cdot\phi(1_R)$ so $\phi(1_R)(1_S-\phi(1_R))=0_S$ and so ...
