What Are the Ring Homomorphisms from Z[X] to Z[X]?

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SUMMARY

The discussion centers on identifying all ring homomorphisms from the polynomial ring Z[X] to itself and to other rings R. Participants emphasize the importance of understanding theorems related to homomorphisms in polynomial rings, suggesting that a general approach may simplify finding solutions. The conversation highlights the necessity of foundational knowledge in ring theory to tackle such problems effectively.

PREREQUISITES
  • Understanding of ring theory concepts
  • Familiarity with polynomial rings, specifically Z[X]
  • Knowledge of ring homomorphisms and their properties
  • Experience with mathematical proofs and theorems related to algebra
NEXT STEPS
  • Study theorems on homomorphisms in polynomial rings
  • Explore examples of ring homomorphisms from Z[X] to other rings
  • Learn about the structure of polynomial rings and their applications
  • Investigate advanced topics in abstract algebra, focusing on ring theory
USEFUL FOR

Mathematicians, students of abstract algebra, and anyone interested in the properties and applications of ring homomorphisms in polynomial rings.

esisk
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what are all the ring homomorphism from Z[X] to Z[X]. Thank you
 
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What are all the ring homomorphisms from Z[X] to R for a ring R? If you can't do that, then you can't do this problem.
 
Dear Hurkyl,
While I (I hope) do see the point behind you remark, quite frankly I do not appreciate it as it is redundant. I am genuinely asking for help and you are conjecturing when one is not able to solve this problem. I thank you
 
It looked like a request for an answer, not a request for help -- it is strictly against our policy to hand out answers to homework problems.

My response was meant in all seriousness -- you should have seen in your class a very powerful theorem about homomorphisms from polynomial rings. And sometimes, it's easier to find/work out a solution when you consider the general case without regard to the specific. I assume from your response that you were able to recall the answer? (or able to track it down in your book?)
 
Okay, thank you. I will review
 

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