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In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the subring Z[a] of K generated by a. Then OK is a quotient of the polynomial ring Z[X] and the powers of a constitute a power integral basis. In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α.

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  • In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the subring Z[a] of K generated by a. Then OK is a quotient of the polynomial ring Z[X] and the powers of a constitute a power integral basis. In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α. (en)
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  • In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the subring Z[a] of K generated by a. Then OK is a quotient of the polynomial ring Z[X] and the powers of a constitute a power integral basis. In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α. (en)
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  • Monogenic field (en)
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