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Square-difference factor absorbing ideals of a commutative ring

David F. Anderson, Ayman Badawi, Jim Coykendall

Abstract

Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if whenever $a^2 - b^2 \in I$ for $0 \neq a, b \in R$, then $a + b \in I$ or $a - b \in I$. In this paper, we introduce and investigate sdf-absorbing ideals.

Square-difference factor absorbing ideals of a commutative ring

Abstract

Let be a commutative ring with . A proper ideal of is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of if whenever for , then or . In this paper, we introduce and investigate sdf-absorbing ideals.
Paper Structure (5 sections, 34 theorems)

This paper contains 5 sections, 34 theorems.

Table of Contents

  1. Introduction
  2. Properties of sdf-absorbing ideals
  3. When every ideal is an sdf-absorbing ideal
  4. Additional results
  5. Weakly square-difference factor absorbing ideals

Key Result

Theorem 2.2

Let $I$ be a nonzero sdf-absorbing ideal of a commutative ring $R$. Then $I$ is a radical ideal of $R$.

Theorems & Definitions (81)

  • Definition 2.1
  • Theorem 2.2
  • proof
  • Remark 2.3
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • proof
  • Theorem 2.6
  • proof
  • ...and 71 more