Results 211 to 220 of about 11,161 (225)
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The College Mathematics Journal, 2010
The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings—by professional mathematicians and undergraduates.
Axtell, Michael, Stickles, Joe
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PRIME ALGEBRAS AND ABSOLUTE ZERO DIVISORS
Mathematics of the USSR-Izvestiya, 1987One of the main problems in the structure theory of any class of algebras is the problem of describing prime algebras in this class. This problem was solved for alternative, Jordan and \((-1,1)\)-algebras (module associative algebras) under the additional assumption of nondegeneracy, where an algebra is called nondegenerate if it does not contain ...
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Journal of Algebra and Its Applications, 2020
Let [Formula: see text] be a commutative ring and [Formula: see text] be the zero divisor graph of [Formula: see text]. In this paper, we investigate when the zero divisor graph is a line graph. We completely present all commutative rings which their zero divisor graphs are line graphs. Also, we study when the zero divisor graph is the complement of a
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Let [Formula: see text] be a commutative ring and [Formula: see text] be the zero divisor graph of [Formula: see text]. In this paper, we investigate when the zero divisor graph is a line graph. We completely present all commutative rings which their zero divisor graphs are line graphs. Also, we study when the zero divisor graph is the complement of a
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On Domination in Zero-Divisor Graphs
Canadian Mathematical Bulletin, 2013AbstractWe first determine the domination number for the zero-divisor graph of the product of two commutative rings with 1. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a
Rad, Nader Jafari +2 more
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Simple Graphs and Zero-divisor Semigroups
Algebra Colloquium, 2009In this paper, we provide examples of graphs which uniquely determine a zero-divisor semigroup. We show two classes of graphs that have no corresponding semigroups. Especially, we prove that no complete r-partite graph together with two or more end vertices (each linked to distinct vertices) has corresponding semigroups.
Wu, Tongsuo, Chen, Li
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Proceedings of the London Mathematical Society, 1982
Small, L. W., Stafford, J. T.
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Small, L. W., Stafford, J. T.
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Krull rings with zero divisors
Communications in Algebra, 1983PORTELLI, DARIO, SPANGHER, WALTER
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