http://www.design-ring.com/rings-fields-and-vector-spaces/
consider a mapping F: x to y?
if x and y are groups, what conditions must F satisfy in order to F to be a group homomorphism?
if x and y are rings (with an identity element), what conditions must F satisfy in order for F to be a ring homomorphism?
if x and y are vector spaces over the same field R, what conditions must F satisfy in order for F to be a vector space homomorphism?
This is asking you if you know the definitions for:
– group homomorphism
– ring homomorphism
– vector space homomorphism
F is a function that maps x to y, which is another way of saying
F(x) = y (where y is some function involving x like 2x + 9).
So what definitions do you have for the above?
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