The intersection graph of annihilator submodules of a module

• Autorzy: Pejman S. B. , Payrovi Sh. , Babaei S.

Identyfikatory

DOI

10.7494/OpMath.2019.39.4.577

• Języki publikacji: EN

Abstrakty

EN

Let R be a commutative ring and M be a Noetherian R-module. The intersection graph of annihilator submodules of M, denoted by GA(M) is an undirected simple graph whose vertices are the classes of elements of [formula], for a, b ∈ R two distinct classes [a] and [b] are adjacent if and only if [formula]. In this paper, we study diameter and girth of GA(M) and characterize all modules that the intersection graph of annihilator submodules are connected. We prove that GA(M) is complete if and only if ZR{M) is an ideal of R. Also, we show that if M is a finitely generated R-module with [formula] and [formula] and GA(M) is a star graph, then r(AnnR(M)) is not a prime ideal of R and [formula].

Słowa kluczowe

EN

prime submodule; annihilator submodule; intersection annihilator graph

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 4
• Strony: 577--588
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Pejman S. B.

• Imam Khomeini International University Department of Mathematics, Faculty of Science P.O. Box: 34148-96818, Qazvin, Iran

autor

Payrovi Sh.

• Imam Khomeini International University Department of Mathematics, Faculty of Science P.O. Box: 34148-96818, Qazvin, Iran

autor

Babaei S.

• Imam Khomeini International University Department of Mathematics, Faculty of Science P.O. Box: 34148-96818, Qazvin, Iran

Bibliografia

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