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Miklos Schweitzer 1976_4

Source: Construct an integral domain over the ring of rational integers

December 30, 2008
calculusintegrationalgebrafunctiondomainpolynomialRing Theory

Problem Statement

Let Z \mathbb{Z} be the ring of rational integers. Construct an integral domain I I satisfying the following conditions: a)Z⫋I \mathbb{Z} \varsubsetneqq I; b) no element of I \minus{} \mathbb{Z} (only in I I) is algebraic over Z \mathbb{Z} (that is, not a root of a polynomial with coefficients in Z \mathbb{Z}); c) I I only has trivial endomorphisms. E. Fried
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