11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if f(x+y)=f(x) + f(y) and f(xy) =f(y)f(x) \ x, y = R. Let f, g be two antihomomorphisms of a ring R into R. Prove that fg: RR is a homomorphism.

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*Ring Homomarphism 

11. Let R and R' be two rings. A mapping f: R→R' is
called an antihomomorphism, if
ƒ (x + y) =f(x) +ƒ(y) and f(xy) =ƒ (y) ƒ (x) \ x, y ɛ R.
1
Let f, g be two antihomomorphisms of a ring R into R. Prove that
fg: R R is a homomorphism.
—
Transcribed Image Text:11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if ƒ (x + y) =f(x) +ƒ(y) and f(xy) =ƒ (y) ƒ (x) \ x, y ɛ R. 1 Let f, g be two antihomomorphisms of a ring R into R. Prove that fg: R R is a homomorphism. —
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