Let R be the set of all real valued functions defined for all reals under function addition and multiplication.(adsbygoogle = window.adsbygoogle || []).push({});

Determine all zero divisors of R.

A zero divisor is a non zero element such that when multiplied with another nonzero element the product is zero.

So I said that the zero divisors of R would be all the functions in R that are not the zero function but take on the value of zero at least one time.

Am I close?

acoording to my answer though f=sin X and g= x-2 would be zero divisors because niether function is the zero function but fg = (sin X)(x-2) = 0 at x=2

but my teacher said this is wrong he said the product has to be zero for all x.

How would I even begin to find all the functions that are not the zero function but when multiplied together is zero for all x?

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# Homework Help: Abstract alg zero divisor?

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