Euclidean Rings of S-integers in Complex Quadratic Fields

Abstract

We give an elementary approach to studying whether rings of S-integers in complex quadratic fields are Euclidean with respect to the S-norm.

MSC:

• 11R11
• 11A05

Acknowledgment

[Acknowledgments] This research was completed as part of the Research Experience for Undergraduates and Teachers program at California State University, Chico funded by the National Science Foundation (DMS-1559788). We thank the editor and the anonymous referee for their helpful comments that improved the quality of this paper.

Additional information

Notes on contributors

Kyle Hammer

Kyle Hammer received his B.S. in Mathematics from California State University, Chico. He is currently a Ph.D. student at the University of Kentucky. His research interests are analysis and partial differential equations.

Department of Mathematics, University of Kentucky, Lexington, 40506

[email protected]

Kevin McGown

Kevin McGown received his Ph.D. in Mathematics from University of California, San Diego. He is currently a Professor at California State University, Chico. His area of research interest is number theory.

Department of Mathematics and Statistics, California State University, Chico, 95929

[email protected]

Skip Moses

Skip Moses received his B.S. in Mathematics from California State University, Chico. He will be pursuing a M.S. degree at California Polytechnic State University, San Luis Obispo. His area of research interest is algebra.

Department of Mathematics and Statistics, California State University, Chico, 95929

[email protected]