# Example sought of an atomic domain R such that R[t] is not atomic

Recall that an integral domain $R$ is atomic if every nonzero nonunit admits at least one factorization into irreducible elements. (Indeed, hard-core factorization theorists have replaced the word "irreducible" by "atom".)

From prior reading, I happen to know that there exist atomic integral domains $R$ such that the univariate polynomial ring $R[t]$ is not atomic. This is a somewhat surprising pathology, because the implication is true if both instances of "atomic" are replaced by "UFD", "Noetherian" or "Ascending Chain Condition on Principal Ideals".

But I don't know a precise example or a reference, and I would like one for an expository article I'm writing. Of course, the chronologically earlier and logically simpler the example, the better.

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+1, but I removed the LaTeX from the title, as it served no purpose, as far as I can tell. –  Harry Gindi May 19 '10 at 9:06

There it was conjectured that $R[X]$ atomic $\implies$ $R[X,Y]$ is also atomic.