About quadratic residues in a class of rings

TL;DR

This paper investigates the structure of invertible quadratic residues in a class of commutative rings with specific ideals, relating their properties to those in quotient rings to deepen understanding of quadratic residue behavior.

Contribution

It introduces a framework connecting quadratic residues in rings with those in their quotient rings, under certain ideal conditions, advancing algebraic residue theory.

Findings

Characterizes invertible quadratic residues in rings via quotient ring properties

Establishes conditions linking residues in rings and quotient rings

Provides new insights into the structure of quadratic residues in algebraic rings

Abstract

Let $R$ be a commutative ring with a collection of ideals $\{ N_1, N_2, \dots, N_{k-1}\}$ satisfying certain conditions, properties of the set of invertible quadratic residues of the ring $R$ are described in terms of properties of the set of invertible quadratic residues of the quotient ring $R/N_1$.