The M-Principal Graph of a Commutative Ring
M.J. Nikmehr, F. Heydari

TL;DR
This paper intended to introduce the M-Principal Graph of a commutative ring, aiming to explore its algebraic and graph-theoretic properties, but was withdrawn due to errors in proofs.
Contribution
The paper proposed a novel graph-theoretic framework for analyzing commutative rings, but was withdrawn before publication.
Findings
Original concept of M-Principal Graph introduced
Theoretical properties discussed but not validated
Potential applications in algebraic graph theory
Abstract
This paper has been withdrawn by the author because there are some typos in proofs.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Commutative Algebra and Its Applications
