THE SUBMODULE-BASED ZERO-DIVISOR GRAPH WITH RESPECT TO SOME HOMOMORPHISM

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BAZIAR M.; RANJBAR N.

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Paper Information

Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2013 | Volume:7 | Issue:2 (S.N. 17) Page(s): 15-24

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Information Journal Paper

Title

THE SUBMODULE-BASED ZERO-DIVISOR GRAPH WITH RESPECT TO SOME HOMOMORPHISM

Author(s)

BAZIAR M. | RANJBAR N. | Issue Writer Certificate

Keywords

ZERO-DIVISOR GRAPH OF MODULES

DIAMETER

CUT-POINT

CLIQUE NUMBER

Abstract

Let M be an R-module and 0¹¦ÎM*=Hom (M, R). The graph G¦ (M) is a graph with vertices Z¦ (M)={x ÎM \ {0} |x¦(y) = 0 or y¦(x) = 0 for some non-zero yÎM}, in which non-zero elements x and y are adjacent provided that x¦(y) = 0 or y¦ (x)=0, which introduced and studied in [3]. In this paper we associate an undirected submodule based graph G¦N (M) for each submodule N of M with vertices Z¦N (M)= {xÎM \ N | x¦(y) ÎN or y¦ (x) ÎN for some y Î M \N}, in which non-zero elements x and y are adjacent provided that x¦ (y)ÎN or y¦(x) ÎN. We observe that over a commutative ring R, G¦N (M) is connected and diam (G¦N (M)) £3. Also we get some results about CLIQUE NUMBER and connectivity number of G¦ N (M).

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APA: Copy

BAZIAR, M., & RANJBAR, N.. (2013). THE SUBMODULE-BASED ZERO-DIVISOR GRAPH WITH RESPECT TO SOME HOMOMORPHISM. JOURNAL OF MATHEMATICAL EXTENSION, 7(2 (S.N. 17)), 15-24. SID. https://sid.ir/paper/645005/en

Vancouver: Copy

BAZIAR M., RANJBAR N.. THE SUBMODULE-BASED ZERO-DIVISOR GRAPH WITH RESPECT TO SOME HOMOMORPHISM. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2013;7(2 (S.N. 17)):15-24. Available from: https://sid.ir/paper/645005/en

IEEE: Copy

M. BAZIAR, and N. RANJBAR, “THE SUBMODULE-BASED ZERO-DIVISOR GRAPH WITH RESPECT TO SOME HOMOMORPHISM,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 7, no. 2 (S.N. 17), pp. 15–24, 2013, [Online]. Available: https://sid.ir/paper/645005/en

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