→ R be a ring homomorphism, where R is a commutat .. bn be some arbitary elements of R. then there ex: /....

Q: Show that f:Z2 -> Z2 defined by f(n) = n2-n is a ring homomarphism.

A: The element in Z2 are {0,1} Now, f(0) = 02 - 0 = 0           f(1) = 12 - 1 = 0 Hence, f maps Z2 to…

Q: Suppose Φ is a ring homomorphism from Z ⨁ Z into Z ⨁ Z. Whatare the possibilities for Φ((1, 0))?

A: Let ϕ be a ring homomorphism from ℤ⊕ℤ into ℤ⊕ℤ. Then, we know that ϕ is a group homomorphism and a…

Q: Find all possible ring homomorphisms o : Z10 --->Z15 (b) In each case identify the Kern

A:

Q: don't understand how phi(a+c)=a+c. Please explain. Thank you

A: Given

Q: Let f: R → S be a ring homomorphism and T ≤ S. Prove that K = { r ∈ R : f (r) = 0s} and P = { r ∈ R…

A:

Q: 5) Let (R,+) and (R.+,) be any two rings, let f: R R be a ring homomorphism Ker () (0), then a) f is…

A: