 Home

Codex Wiki

Mathematics

Area of mathematics

Algebra

Algebraic number theory

Cubic field of discriminant minus 307

For $g(X)=X^3-5X^2+11X-12$, the reductions are
$$
\overline g=X(X^2+X-1)\quad\text{over }\mathbb F_3
$$
and
$$
\overline g=X(X^2+X+1)\quad\text{over }\mathbb F_2.
$$
Both quadratic factors are irreducible, so
$$
(3)=(3,\beta)(3,\beta^2+\beta-1)
$$
and
$$
(2)=(2,\beta)(2,\beta^2+\beta+1).
$$


Prime ideals above two and three in the cubic field of discriminant minus 307

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 20G / c / Solution

Prime ideals above two and three in the cubic field of discriminant minus 307

 Ancestors (6)

 Incoming links (1)

 Discussion (0)

 Articles by others on the same topic (0)

Prime ideals above two and three in the cubic field of discriminant minus 307

 Ancestors (6)

 Incoming links (1)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)