Can someone provide me with an example of a ring that is not atomic, that is, there is an element that has no finite factorization in irreducibles?
2026-03-21 02:42:59.1774060979
Non atomic ring example
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Let $R = \mathbb Q[ x, x^\frac12,x^\frac 1 3\ldots ]$, the ring of polynomials with fractional exponents. Now try factoring $x$ which is not a unit in $R$ because it’s inverse would have to have an exponent of negative degree.