# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

## Class groups of global function fields with certain splitting behaviors of the infinite primeHTML articles powered by AMS MathViewer

by Yoonjin Lee
Proc. Amer. Math. Soc. 137 (2009), 415-424 Request permission

## Abstract:

For certain two cases of splitting behaviors of the prime at infinity with unit rank $r$, given positive integers $m, n$, we construct infinitely many global function fields $K$ such that the ideal class group of $K$ of degree $m$ over $\mathbb {F}(T)$ has $n$-rank at least $m-r-1$ and the prime at infinity splits in $K$ as given, where $\mathbb {F}$ denotes a finite field and $T$ a transcendental element over $\mathbb {F}$. In detail, for positive integers $m$, $n$ and $r$ with $0 \le r \le m-1$ and a given signature $(e_i, \mathfrak {f}_i)$, $1 \le i \le r+1$, such that $\sum _{i=1}^{r+1}{e_i\mathfrak {f}_i} =m$, in the following two cases where $e_i$ is arbitrary and $\mathfrak {f}_i =1$ for each $i$, or $e_i =1$ and $\mathfrak {f}_i$’s are the same for each $i$, we construct infinitely many global function fields $K$ of degree $m$ over $\mathbb {F}(T)$ such that the ideal class group of $K$ contains a subgroup isomorphic to $(\mathbb {Z}/n\mathbb {Z})^{m-r-1}$ and the prime at infinity ${\wp _\infty }$ splits into $r+1$ primes $\mathfrak {P}_1, \mathfrak {P}_2, \cdots , \mathfrak {P}_{r+1}$ in $K$ with $e(\mathfrak {P}_i/{\wp _\infty }) = e_i$ and $\mathfrak {f}(\mathfrak {P}_i/{\wp _\infty }) = \mathfrak {f}_i$ for $1 \le i \le r+1$ (so, $K$ is of unit rank $r$).
References
Similar Articles
• Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11R29, 11R58
• Retrieve articles in all journals with MSC (2000): 11R29, 11R58
• Yoonjin Lee
• Affiliation: Department of Mathematics, Ewha Womans University, Seoul, 120-750, Republic of Korea
• MR Author ID: 689346
• ORCID: 0000-0001-9510-3691
• Email: yoonjinl@ewha.ac.kr
• Received by editor(s): April 26, 2007
• Published electronically: October 6, 2008
• Additional Notes: This work was supported by the Ewha Womans University Research Grant of 2007
• Communicated by: Wen-Ching Winnie Li