Problem 5. Suppose that R = (R, +,*) and S = (S, +,*) are rings, and suppose that f : R – S is a ring homomorphism that is onto. Part (a). If a E R…
Get perfect grades by consistently using our affordable writing services. Place your order and get a quality paper today. Take advantage of our current 20% discount by using the coupon code GET20
Order a Similar Paper Order a Different Paper
Solve problem 5 which is on Abstract Algebra. Question is based on Quotient Rings.
- Attachment 1
- Attachment 2
Problem 5. Suppose that R = (R, +,*) and S = (S, +,*) are rings, and suppose that f : R – S is a ringhomomorphism that is onto.Part (a). If a E R and x E a + ker(f), prove that f (x) = f (a).Part (b). If a, b E R are such that f (a) = f(b), prove that a – b E ker(f).Part (c). If a, b E R are such that f (a) = f(b), use Part (b) to prove that a + ker(f) = b + ker(f).Part (d). Define a function Of : LCker(/) – S according to the rule of (a + ker(f)) = f (a). Prove thatOr is a bijection.Part (e). Prove that Or is a ring isormorphism.
Have your paper completed by a writing expert today and enjoy posting excellent grades. Place your order in a very easy process. It will take you less than 5 minutes. Click one of the buttons below.
Order a Similar Paper Order a Different Paper