Denote Zn = (y) = {e, v, ..., yn-1} (where y = e). Using this notation:...

Transcribed Image Text:

Denote Zn = (y) = {e, v, ..., yn-1} (where y = e). Using this notation: Y₂ (a) Prove that for any unital ring R, there is a surjective homomorphism R[x] → RZn that sends a E R to ae E RZn and sends x to ly € RZn. (b) Describe the kernel of the homomorphism found in (a). (Justify your answer carefully!) Denote Zn = (y) = {e, v, ..., yn-1} (where y = e). Using this notation: Y₂ (a) Prove that for any unital ring R, there is a surjective homomorphism R[x] → RZn that sends a E R to ae E RZn and sends x to ly € RZn. (b) Describe the kernel of the homomorphism found in (a). (Justify your answer carefully!)

Answer rating: 100% (QA)

a Define a map f R Rn by sending a R to the ntuple a a a Rn That is the ith component of fa is simpl... View the full answer