Let d be a prime with   and  which is an order in the ring  of integers of K. Using the bijection between matrix conjugations over  with characteristic polynomial  and -ideal classes, we study the relation between -ideal class group and -ideal class group. Assume that d satisfies the condition: if  with a even, then  or  is an odd prime. Then we prove that the class number of K is one.

class number, real quadratic field.

Received: April 5, 2022; Accepted: May 19, 2022; Published: May 25, 2022

How to cite this article: Anly Li, On class number one for the real quadratic field , JP Journal of Algebra, Number Theory and Applications 55 (2022), 79-84. http://dx.doi.org/10.17654/0972555522021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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