• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.657-660
• /
• 2019

We give necessary and sufficient condition for the Greenberg's generalized conjecture conjecture on certain imaginary quadratic fields.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.23-27
• /
• 2004

In this paper we explicitly compute the orders of ambiguous ideal class groups of layers of the basic ${\mathbb{Z}}_3-extension$ of certain cubic fields and give an example for Greenberg's conjecture.

• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.267-269
• /
• 2021

A finitely generated torsion module M for ℤ_p[[T, T₂, ⋯ , T_d]] is pseudo-null if M/TM is pseudo-null over ℤ_p[[T₂, ⋯ , T_d]]. This result is used as a tool to prove the generalized Greenberg's conjecture in certain cases. The converse may not be true. In this paper, we give examples of pseudo-null Iwasawa modules whose reduction are not pseudo-null.