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TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL

Mehdi Khoramdel|Shahabaddin Ebrahimi Atani|Saboura Dolati Pish Hesari
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회지 (Journal of the KMS)|제52권 제1호|pp. 159-176

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참고문헌

키워드

strong co-idealtotal identity-summand graphidentity-sum- mand graph based a co-idealtotal identity-summand graph based a co-ideal
주제분류수학

초록

Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if xy ∈ S(I).

Abstract

Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if xy ∈ S(I).

참고문헌 (17)

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관련 논문AI추천

TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTSMehdi Khoramdel, Saboura Dolati Pish Hesari, Shahabaddin Ebrahimi Atani대한수학회 · 대한수학회지2014 · 제51권 제3호THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGSMehdi Khoramdel, Saboura Dolati Pish Hesari, Shahabaddin Ebrahimi Atani대한수학회 · 대한수학회지2014 · 제51권 제1호The total graph of a commutative ring with respect to proper idealsAhmad Abbasi, Shokoofe Habibi대한수학회 · 대한수학회지2012 · 제49권 제1호On Comaximal Graphs of Near-ringsBalasubramanian Elavarasan, Patchirajulu Dheena경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호A generalized ideal based-zero divisor graphs of near-ringsBalasubramanian Elavarasan, Patchirajulu Dheena대한수학회 · 대한수학회논문집2009 · 제24권 제2호Zero-divisor graphs with respect to primal and weakly primal idealsAhamd Yousefian Darani, Shahabaddin Ebrahimi Atani대한수학회 · 대한수학회지2009 · 제46권 제2호

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