I have the following exercise: "Let $S$ be an arbitrary set and $K$ a field. Show that the polynomial ring $K[S]$ is a unique factorization domain." My question is, how one defines such a polynomial ring? Every element as a variable? There are no conditions on cardinality of this set.
2026-04-06 05:49:46.1775454586
Polynomial ring over an arbitrary set
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