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- W2615924063 abstract "Abstract Let R be a ring with identity and M be a unitary left R -module. The intersection graph of submodules of M , denoted by G ( M ), is defined to be a graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have non-zero intersection. In this paper, we consider the intersection graph of submodules of a module. We determine the structure of modules whose clique numbers are finite. We show that if 1 < ω ( G ( M )) < ∞, then M is a direct sum of a finite module and a cyclic module, where ω ( G ( M )) denotes the clique number of G ( M ). We prove that if ω ( G ( M )) is not finite, then M contains an infinite clique. Among other results, it is shown that a Noetherian R -module whose intersection of all non-trivial submodules is non-zero, is Artinian." @default.
- W2615924063 created "2017-05-26" @default.
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- W2615924063 date "2017-04-01" @default.
- W2615924063 modified "2023-09-27" @default.
- W2615924063 title "Some results on the intersection graph of submodules of a module" @default.
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- W2615924063 doi "https://doi.org/10.1515/ms-2016-0267" @default.
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