Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Prufer domain is a type of commutative ring that generalizes Dedekind domains in a non-Noetherian context. These rings possess the nice ideal and module theoretic properties of Dedekind domains, but usually only for finitely generated modules. Prufer domains are named after the German mathematician Heinz Prufer. The ring of entire functions on the open complex plane C form a Prufer domain. The ring of integer valued polynomials with rational number coefficients is a Prufer domain. While every number ring is a Dedekind domain, their union, the ring of algebraic integers, is a Prufer domain. Just as a Dedekind domain is locally a discrete valuation ring, a Prufer domain is locally a valuation ring, so that Prufer domains act as non-noetherian analogues of Dedekind domains. Indeed the direct limit of Prufer domains is a Prufer domain, (Fuchs

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