Results 211 to 220 of about 88,501 (223)

Zero-divisors and zero-divisor graphs of power series rings [PDF]

open access: possibleRicerche di Matematica, 2015
Let R be a commutative ring with identity, Z(R) its set of zero-divisors and N(R) its nilradical. The zero-divisor graph of R denoted by $$\varGamma (R)$$ , is the graph with vertices
Ali Benhissi, Amor Haouaoui
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Graphs and Zero-Divisors

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 rings where zero-divisor polynomials have zero-divisor coefficients

Rocky Mountain Journal of Mathematics, 2021
Based on McCoy’s theorem on commutative rings, Nielsen called a ring R right McCoy if the equation f(x)g(x)=0 implies f(x)c=0 for some nonzero element c in R, where f(x) and g(x) are nonzero polynomials in R[x]. In this paper, a class of rings is introduced and called ZPZC rings, containing McCoy rings, and then their properties are investigated. Also,
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Remarks on Divisors of Zero

The American Mathematical Monthly, 1942
(1942). Remarks on Divisors of Zero. The American Mathematical Monthly: Vol. 49, No. 5, pp. 286-295.
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Divisors of Zero in Polynomial Ring

The American Mathematical Monthly, 1943
(1943). Divisors of Zero in Polynomial Rings. The American Mathematical Monthly: Vol. 50, No. 1, pp. 7-8.
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Irreducible Divisor Graphs in Commutative Rings with Zero Divisors

Communications in Algebra, 2008
In their article “Irreducible Divisor Graphs”, Coykendall and Maney (2007) introduced the idea of irreducible divisor graphs of elements of a domain. We generalize this concept to commutative rings with zero divisors. In particular, the interplay of unique factoring and connected/complete graphs is explored.
Axtell, Michael, Stickles, Joe
openaire   +3 more sources

Krull rings with zero divisors

Communications in Algebra, 1983
PORTELLI, DARIO, SPANGHER, WALTER
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