Remarks on principal factors in a relative cubic field

DOI10.1016/0022-314X(71)90040-0zbMath0218.12002MaRDI QIDQ2546532

Harvey Cohn, Pierre Barrucand

Publication date: 1971

Published in: Journal of Number Theory (Search for Journal in Brave)

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16)

Related Items (25)

Tame kernels of pure cubic fields ⋮ On the units of cubic and bicubic fields ⋮ Principal factors in a pure cubic field and its unramified cyclic cubic extensions ⋮ The generators of $3$-class group of some fields of degree $6$ over $\mathbb{Q}$ ⋮ Improving the Speed of Calculating the Regulator of Certain Pure Cubic Fields ⋮ PRINCIPAL FACTORS AND LATTICE MINIMA IN CUBIC FIELDS ⋮ Ranks of Sylow 3-subgroups of ideal class groups of certain cubic fields ⋮ Structure of relative genus fields of cubic Kummer extensions ⋮ A unit relationship for pure sextic fields ⋮ The 3‐class groups of non‐Galois cubic fields—I ⋮ The 3‐class groups of non‐Galois cubic fields–II ⋮ 3-rank of ambiguous class groups of cubic Kummer extensions ⋮ On a conjecture of Lemmermeyer ⋮ Eine Bemerkung über kubische Einheiten ⋮ Rational compositum genus for a pure cubic field ⋮ Einige Bemerkungen zu Einheiten in reinen kubischen Körpern ⋮ Units in totally complex \(S_3\) fields ⋮ Units and class numbers of a dihedral Galois extension of \(\mathbb{Q}\) ⋮ Pure fields of degree 9 with class number prime to 3 ⋮ The Simplest Cubic Fields ⋮ Differential principal factors and Pólya property of pure metacyclic fields ⋮ On 3-Class groups of certain pure cubic fields ⋮ Fields ℚ(d3,ζ3) whose 3-class group is of type (9,3) ⋮ The 3-class groups of \(\mathbb{Q}(\sqrt[3{p})\) and its normal closure] ⋮ A note on ramified principal ideals in a non-Galois cubic field

Cites Work

• A rational genus, class number divisibility, and unit theory for pure cubic fields
• Pure cubic fields whose class numbers are multiples of three
• The rational solutions of the diophantine equation \(Y^2=X^3-D\)
• Sufficient congruence conditions for the existence of rational points on certain cubic surfaces
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