Zero divisors

Zero divisors

Integral Domains, Ideals, and Unique Factorization

Published in Richard A. Mollin, Algebraic Number Theory Second, 2011

An integral domain is a commutative ring D with identity 1D, having no zero divisors. In particular, if every nonzero element is a unit, then D is a field.

Wiener Index of Some Zero-Divisor Graphs

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Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020

S. K. Vaidya, M. R. Jadeja

A zero-divisor in a ring R is an element x for which ∃y≠0 in R such that xy = 0.

A discrete variant of Farkas' lemma and related results

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Journal Information

Published in Optimization, 2021

David Bartl

Observe that an element with is a zero divisor if and only if n<1. However, there is no universal zero divisor in the ring R. Moreover, Hypothesis 4.1 is satisfied with any element for any . Indeed, if , then we must have , and , therefore because , etc.

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Integral Domains, Ideals, and Unique Factorization

Wiener Index of Some Zero-Divisor Graphs

A discrete variant of Farkas' lemma and related results