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Some graphs arising from derivations
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Let R be a ring and d a derivation of R. The graph Γ_d(R) of R is defined as the graph with vertices set R, and two distinct vertices x and y are adjacent if and only if [d(x), d(y)] + d[x, y] − [x, y] = 0. In this paper, we study the interaction between some ring-theoretic properties of R and certain graph-theoretic properties of Γ_d(R).
Abstract
Let R be a ring and d a derivation of R. The graph Γ_d(R) of R is defined as the graph with vertices set R, and two distinct vertices x and y are adjacent if and only if [d(x), d(y)] + d[x, y] − [x, y] = 0. In this paper, we study the interaction between some ring-theoretic properties of R and certain graph-theoretic properties of Γ_d(R).
참고문헌 (10)
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- E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
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