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Zero divisor graphs for S-act

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Abstract

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(Γ*(A)) ≤ 3; and

  2. (2)

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

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References

  1. J. Ahsan and L. Zhongkui, Math. J. Ibaraki 33, 9 (2001).

    Article  MATH  Google Scholar 

  2. D. F. Anderson and S. Livingston, J. Algebra 217, 434–447 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  3. D. F. Anderson, R. Levy, and J. Shapiro, J. Pure Applied Algebra 180, 221–241 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Beck, J. Algebra 116, 208–226 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Cannon, K. Neuerburg, and S. Redmond, in: Nearrings and Nearfields, Ed. by H. Kiechle, A. Kreuzer, and M. J. Thomsen (Springer, Dordrecht, 2005), pp. 189–200.

  6. M. Behboodi, J. Commutative Algebra 4(2), 175–197 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  7. A. A. Estaji, Arch. Math. (BRNO) Tomus 44, 69–76 (2008).

    MATH  MathSciNet  Google Scholar 

  8. A. A. Estaji and M. Shabani, Far East J. Mathematical Sciences 33, 133–150 (2010).

    MathSciNet  Google Scholar 

  9. A. A. Estaji and S. Tajnia, Lobachevskii J. Mathematics 32(4), 358–365 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  10. F. R. DeMeyer, T. McKenzie, and K. Schneider, Semigroup Forum 65, 206–214 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  11. Mati Klip, Ulrich Knauer, and Alexander V. Mikhalev, Monoids, Acts and Categories With Applications to Wreath Products and Graphs (Walter de Gruyter, Berlin-New York, 2000).

    Book  Google Scholar 

  12. Miao Zuo and Tongsuo Wu, Semigroup Forum 70, 71–80 (2005).

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran

    A. A. Estaji & A. As. Estaji

  2. Faculty of Basic Sciences, Birjand University of Technology, Birjand, Iran

    T. Haghdadi

Authors
  1. A. A. Estaji
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  2. T. Haghdadi
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  3. A. As. Estaji
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Correspondence to A. A. Estaji.

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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). https://doi.org/10.1134/S1995080215010084

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  • DOI: https://doi.org/10.1134/S1995080215010084

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