Square-difference factor absorbing ideals of a commutative ring

David F. Anderson; Ayman Badawi; Jim Coykendall

Square-difference factor absorbing ideals of a commutative ring

Commutative Algebra 2024-03-01 v1

Authors: 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.

Keywords

monomial ideals commutative ring theory ideal theory

Cite

@article{arxiv.2402.18704,
  title  = {Square-difference factor absorbing ideals of a commutative ring},
  author = {David F. Anderson and Ayman Badawi and Jim Coykendall},
  journal= {arXiv preprint arXiv:2402.18704},
  year   = {2024}
}

Comments

18 pages

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