SOME RESULTS ON THE COMPLEMENT OF THE ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING
2011 ◽
Vol 10
(03)
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pp. 573-595
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Let R be a commutative ring with identity admitting at least two nonzero zero-divisors. First, in this article we determine when the complement of the zero-divisor graph of R is connected and also determine its diameter when it is connected. Second, in this article we study the relationship between the connectedness of the complement of the zero-divisor graph of R to that of the connectedness of the complement of the zero-divisor graph of T where either T = R[x] or T = R[[x]] and we study the relationship between their diameters in the case when both the graphs are connected. Finally, we give some examples to illustrate some of the results proved in this article.
2019 ◽
Vol 19
(08)
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pp. 2050155
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2012 ◽
Vol 55
(1)
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pp. 127-137
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2007 ◽
Vol 2007
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pp. 1-15
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2020 ◽
Vol 12
(1)
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pp. 84-101
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2019 ◽
Vol 18
(10)
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pp. 1950190
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2016 ◽
Vol 16
(07)
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pp. 1750132
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