Adjacency-like conditions and induced ideal graphs

Abstract

In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph theoretic structure of the associated graph. Behavior of these graphs under standard ring extensions are studied, and in conjunction with the theory, some classical results and connections are made.

KEYWORDS:

• Noetherian
• SFT

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13C05
• 13A15
• 13C13

Acknowledgments

The authors thank the referee of this paper for a very thorough reading and insightful comments that greatly improved the presentation of this work.