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Reference.org
Monogenic field
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a monogenic field is an <a href="/facts/Algebraic_number_field/e0K0TXSh">algebraic number field</a> <i>K</i> for which there exists an element <i>a</i> such that the <a href="/facts/Ring_of_integers/KEzxxMbh">ring of integers</a> <i>O</i><i>K</i> is the subring Z[<i>a</i>] of <i>K</i> generated by <i>a</i>. Then <i>O</i><i>K</i> is a quotient of the <a href="/facts/Polynomial_ring/ua3vk8Ih">polynomial ring</a> Z[<i>X</i>] and the powers of <i>a</i> constitute a power integral basis. </p><p>In a monogenic field <i>K</i>, the <a href="/facts/Discriminant_of_an_algebraic_number_field/mvv6MWKj">field discriminant</a> of <i>K</i> is equal to the <a href="/facts/Discriminant/0SmQtrvU">discriminant</a> of the <a href="/facts/Minimal_polynomial_(field_theory)/dJv9Q0Kh">minimal polynomial</a> of α. </p>