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Description of finite nonnilpotent rings with planar zero-divisor graphs
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A. S. Kuzmina
Published/Copyright:
January 11, 2010
Abstract
The zero-divisor graph of an associative ring R is a graph whose vertices are all nonzero (one-sided and two-sided) zero divisors of R, two distinct vertices x, y are connected by an edge if and only if xy = 0 or yx = 0.
In this paper, all finite nonnilpotent rings with planar zero-divisor graphs are completely described. In the previous paper by Kuzmina and Maltsev, the finite nilpotent rings with planar zero-divisor graphs were studied. Thus, this paper completes the description of finite rings with planar zero-divisor graphs.
Received: 2009-04-25
Revised: 2009-05-05
Published Online: 2010-01-11
Published in Print: 2009-December
© de Gruyter 2009
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Articles in the same Issue
- On quantum realisation of Boolean functions by the fingerprinting technique
- On the choice of the defence strategy for an authentication code with two-state source
- A parametric model of embedding and its statistical analysis
- On some equations related to the tpp-groups
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- Rings over which all finitely generated modules are ℵ0-injective
- On the number of boundary classes in the 3-colouring problem
- Periods of output sequences of an automaton for a given periodic input sequence
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