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For a *-ring A, we associate a simple undirected graph Γ*(A) having all nonzero left zero-divisors of A as vertices and, two vertices x and y are adjacent if xy*… Click to show full abstract
For a *-ring A, we associate a simple undirected graph Γ*(A) having all nonzero left zero-divisors of A as vertices and, two vertices x and y are adjacent if xy* = 0. In case of Artinian *-rings and Rickart *-rings, characterizations are obtained for those *-rings having Γ*(A) a complete graph or a star graph, and sufficient conditions are obtained for Γ*(A) to be connected and also for Γ*(A) to be disconnected. For a Rickart *-ring A, we characterize the girth of gr(Γ*(A)) and prove a sort of Beck’s conjecture.
Keywords:
divisor graph;
zero divisor;
graph ring;
ring involution;
graph
Journal Title: Journal of Algebra and Its Applications
Year Published: 2017
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!