A polynomial ring over a field is a mathematical structure consisting of polynomials whose coefficients come from a given field. This ring is denoted as $F[x]$, where $F$ is the field and $x$ is an indeterminate. Polynomial rings exhibit important algebraic properties, such as being a unique factorization domain (UFD) and having well-defined ideals, which play a crucial role in the study of algebraic structures like Dedekind domains.
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