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The research aims to explore the unit group of cubic number fields and identify fundamental units under specific conditions.

April 4, 2026Open Access

On the unit groups and the ideal class groups of certain cubic number fields

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The research aims to explore the unit group of cubic number fields and identify fundamental units under specific conditions.
Analyzed the cubic polynomial f(x) = x³ + 3x + a³ with a belonging to integers (Z).
Investigated the unit group of the field generated by the real root of the polynomial.
Considered conditions under which specific values become fundamental units.
Identified that u = 1 - a² - a serves as a fundamental unit under certain conditions.
Examined the structure of the 3-class group of the cubic number field.

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Research examines unit groups and ideal class groups in cubic number fields, indicating important algebraic structures.

Eiji Yoshida (2003) studied this question.

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