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In this article, the author gives the following counterexample for "a associates b" but not "a strongly associates b" at the end of the first page. However, in $[1,2]$ , the values of both $x,y$ are zero, so there is no need for choosing $c(t) = 3- 2t$ in that interval, i.e choosing $c(t) = 1 $ in $[1,2]$ is also a possible choice, and in the latter case, $c$ is a unit element of $C[0,3]$ which invalidates this "counterexample". Considering the fact that this article is read by many mathematicians and published, what is wrong in my view that this example is still a counterexample ?
abstract-algebra ring-theory
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