An important historical example is the difficult evolution of the correct definition of "integer" in algebraic extensions, i.e. defining algebraic integers. It was only with great difficulty that Dedekind discovered the the necessity of passing to integrally closed extensions in order to obtain nice factorization theories. Similar struggles were encountered while distilling the correct notion of integral elements for quaternion rings.
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An important historical example is the difficult evolution of the correction notion correct definition of "integer" in algebraic integerextensions, i.e. defining algebraic integers. It was only with great difficulty that Dedekind discovered the the necessity of passing to integrally closed extensions in order to obtain nice factorization theories. Similar difficulties struggles were encountered for while distilling the correct notion of integral quaternionselements for quaternion rings. |
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An important historical example is the difficult evolution of the correction notion of algebraic integer. It was only with great difficulty that Dedekind discovered the the necessity of passing to integrally closed extensions in order to obtain nice factorization theories. Similar difficulties were encountered for integral quaternions. |
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