• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.517-523
• /
• 2013

In this paper we study the infiniteness of Hilbert 3-class field tower of real cubic function fields over $\mathbb{F}_q(T)$, where $q{\equiv}1$ mod 3. We also give various examples of real cubic function fields whose Hilbert 3-class field tower is infinite.

• Korean Journal of Mathematics
• /
• v.26 no.2
• /
• pp.293-297
• /
• 2018

In the paper [4], we constructed 3-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by 3. In this paper, we extend the result for any odd prime p.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.597-601
• /
• 2012

In this paper we study the density of imaginary cubic function fields having the infinite Hilbert 3-class field tower.

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.219-226
• /
• 2014

In this paper we study the infiniteness of Hilbert 2-class field towers of real quadratic function fields over $\mathbb{F}_q(T)$, where q is a power of an odd prime number.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.1049-1060
• /
• 2013

In this paper we study the infiniteness of Hilbert 2-class field towers of imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.

• Korean Journal of Mathematics
• /
• v.20 no.4
• /
• pp.477-483
• /
• 2012

In this paper we study the infiniteness of the Hilbert ${\ell}$-class field tower of imaginary ${\ell}$-cyclic function fields when ${\ell}{\geq}5$.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.161-166
• /
• 2013

In this paper we study the infiniteness of the Hilbert 3-class field tower of imaginary cubic function fields.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.699-704
• /
• 2010

In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.747-756
• /
• 2007

In this paper we give an example of imaginary quadratic number field k such that every ideal of k becomes principal in some proper subfields of the Hilbert class field of k.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.79-87
• /
• 2013

In this paper we study the infniteness of Hilbert 2-class field towers of inert imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.