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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) +f (y) and f (xy) =fV)f (x) , y e R. Let f, g be two antihomomorphisms of a ring R into R. Prove that A 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 f (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 that A fg : R → R is a homomorphism. |
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