On graphs associated with modules over commutative rings (Q2821950)
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scientific article; zbMATH DE number 6629731
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On graphs associated with modules over commutative rings |
scientific article; zbMATH DE number 6629731 |
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26 September 2016
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module
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zero-divisor graph
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ring
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metric dimension
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multiplication-like module
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On graphs associated with modules over commutative rings (English)
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Let $R$ be a commutative ring with unity and $M$ an $R$-module. On this paper the authors associate three graphs to $M$, and relate the properties of these objects. The authors prove, for instance, that the metric dimension of one of the graphs is finite if and only if $M$ is finite over $R$ and that if $M$ is a multiplication-like $R$-module then the three graphs are the same.
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