Ring Homomarphism show* 11. Let R and R’ be two rings. A mapping f:R→R'iscalled an antihomomorphism, iff (x + y) =f (x) +f (y) and f (xy) =fV)f (x) , y e R.Let f, g be two antihomomorphisms of a ring R into R. Prove thatAfg : R → R is a homomorphism.|

Let x, y ∈ R. Then (g)(x + y) = f(g(x + y)) = f(g(x) + g(y)) = f(g(x)) + f(g(y)) =(fg)(x)+(fg)(y),…

Answered: 11. Let R and R' be two rings. A…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 14E: 14. Let be a ring with unity . Verify that the mapping defined by is a homomorphism.

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11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if f (x +y) =f (x) +fv) and f(xry) =fV)f (x) V x, y e R. Let f, 8 be two antihomomorphisms of a ring R into R. Prove that fg : R →R is a homomorphism.