Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

video

Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

sound

Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Persian Version

Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

View:

289
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Download:

166
Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Cites:

Information Journal Paper

Title

tHE ZERO-DIVISOR GRAPH OF A MODULE

Pages

  155-171

Abstract

 Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say 􀀀 (RM), such that when M = R, 􀀀 (RM) coincide with the Zero-divisor graph of R. Many well-known results by D. F. Anderson and P. S. Livingston, have been generalized for 􀀀 (RM). We will show that 􀀀 (RM) is connected with diam(􀀀 (RM))  3, and if 􀀀 (RM) contains a cycle, then gr(􀀀 (RM))  4. We will also show that 􀀀 (RM) = ∅ if and only if M is a prime module. Among other results, it is shown that for a Reduced module M satisfying DCC on cyclic submodules, gr (􀀀 (RM)) = 1 if and only if 􀀀 (RM) is a star graph. Finally, we study the Zero-divisor graph of free R-modules.

Cites

  • No record.

    • References

  • No record.

    • Cite

    APA: Copy

    NAGHIPOUR, A.R.. (2017). tHE ZERO-DIVISOR GRAPH OF A MODULE. JOURNAL OF ALGEBRAIC SYSTEMS, 4(2 ), 155-171. SID. https://sid.ir/paper/718804/en

    Vancouver: Copy

    NAGHIPOUR A.R.. tHE ZERO-DIVISOR GRAPH OF A MODULE. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2017;4(2 ):155-171. Available from: https://sid.ir/paper/718804/en

    IEEE: Copy

    A.R. NAGHIPOUR, “tHE ZERO-DIVISOR GRAPH OF A MODULE,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 4, no. 2 , pp. 155–171, 2017, [Online]. Available: https://sid.ir/paper/718804/en

    Related Journal Papers

  • No record.

    • Related Seminar Papers

  • No record.

    • Related Plans

  • No record.

    • Recommended Workshops






    Move to top