Study of the group of equivalence classes of quadratic ideals for some types of quadratic algebraic fields

Abstract

This article aims to study the quadratic algebraic fields of the type (R-D) for some special values ​​of d, as we know that the fields of the type (R-D) if d≠5, where is a positive square-free integer satisfying then the quadratic field is a real quadratic field of the Richard-Degert type and we denote it by the symbol (R-D).  This pattern has attracted the interest of many researchers, as Mishra, Hogue, and Chakarborty studied the structure of the group of order 4 for quadratic fields of the type  in 2021. In 2020, Hogue and Kotyada studied the problem of the uniqueness of the analysis for fields of the type ). In 2016, Biro, Kim, and Labkova studied the problem of the uniqueness of the analysis for quadratic fields of the type  In this research, we studied these fields for d  where p is a prime number & t is a positive square-free integer