Co-intersection graph of submodules of a module

Let M be a unitary left R-module where R is a ring with identity. The co-intersection graph of proper submodules of M, denoted by Ω(M), is an undirected simple graph whose the vertex set V(Ω) is a set of all non-trivial submodules of M and there is an edge between two distinct vertices N and K if an...

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Збережено в:
Бібліографічні деталі
Дата:2016
Автори: Mahdavi, L.A., Talebi, Y.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2016
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/155196
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Co-intersection graph of submodules of a module / L.A. Mahdavi, Y. Talebi // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 128-143. — Бібліогр.: 11 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме:Let M be a unitary left R-module where R is a ring with identity. The co-intersection graph of proper submodules of M, denoted by Ω(M), is an undirected simple graph whose the vertex set V(Ω) is a set of all non-trivial submodules of M and there is an edge between two distinct vertices N and K if and only if N+K≠M. In this paper we investigate connections between the graph-theoretic properties of Ω(M) and some algebraic properties of modules . We characterize all of modules for which the co-intersection graph of submodules is connected. Also the diameter and the girth of Ω(M) are determined. We study the clique number and the chromatic number of Ω(M).