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Zero divisor graphs for S-act


Let S always denote a semigroup with zero. This paper is devoted to study some of properties zero-divisor graph of S-act. We give several generalizations of the concept of zero-divisor elements in an S-act. Then for each S-act A we associate three undirected (simple) graphs Γ*(A) ⊆ Γ(A) ⊆ Γ*(A). Also we show that if A is an S-act, then

  1. (1)

    Γ*(A) is a connected graph and diam*(A)) ≤ 3; and

  2. (2)

    If Ann(A) is a prime ideal of S, then diam*(A)) ≤ 2.

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Correspondence to A. A. Estaji.

Additional information

Submitted by M. M. Arslanov

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Estaji, A.A., Haghdadi, T. & Estaji, A.A. Zero divisor graphs for S-act. Lobachevskii J Math 36, 1–8 (2015).

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Keywords and phrases

  • semigroup
  • prime subact
  • multiplication S-act
  • zero-divisor graph