THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS

By R. Levy, Jay Shapiro. 2002

93 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c04bffbeba2d1ab62fcecb115cf19ef34cbd975b

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In Algebra and Number Theory

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Citations in the corpus

Von Neumann Regular and Related Elements in Commutative Rings (2012, background): “The zero-divisor graphs of von Neumann regular rings and Boolean rings have been studied in [26], [9], [21], [22] and [23].”
An Ideal-Based Zero-Divisor Graph of a Commutative Ring (2003, background): “The zero-divisor graph of a commutative ring is further examined in Anderson et al. (preprint, 2001), Levy and Shapiro (2002) and Mulay (2002).”
ON THE DIAMETER AND GIRTH OF A ZERO-DIVISOR GRAPH (2007, background): “Following [11], we say that distinct vertices a and b in a graph G are orthogonal, written a⊥b, if a and b are adjacent and there is no vertex c which is adjacent to both a and b, i.”
Zero-divisor graphs, von Neumann regular rings, and Boolean algebras (2003, methodology): “) Also, as in [18], for distinct vertices a and b of G, we say that a and b are orthogonal, written a ⊥ b, if a and b are adjacent and there is no vertex c of G which is adjacent to both a and b, i.”
Zero-Divisor Graph with Respect to an Ideal (2006, background): “…Iran S. Yassemi Department of Mathematics and Computer Science, Faculty of Science, University of Tehran, Tehran, Iran and School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran LetR be a commutative ring with nonzero identity and let I be an ideal ofR.”
Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph (2012, background): “As defined in [20,4], two distinct vertices v and w of a graph Γ are called complements in Γ , written v ⊥ w, if v and w are adjacent, and no vertex of Γ is adjacent to both v and w.”
When a zero-divisor graph is planar or a complete r-partite graph (2003, unknown): “For an extended list of references and the history of this topic the reader is referred to [1–4 ,6, 8 Anderson and Livingston showed in [3, Theorem 2.4] that any two vertices in Γ (R) are connected by a path of length (number of edges) less than or equal to three, consequently Γ (R) is connected;…”