The Probability that the Product of three Elements in a Finite Ring is Zero

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Abstract

Let Formula: see text be a finite commutative ring. In this paper, we consider the probability that the product of randomly chosen three elements of Formula: see text is zero, which we denote by Formula: see text. First we obtain bounds for Formula: see text for various classes of rings and then show that for any ring Formula: see text with identity Formula: see text. Finally, we characterize all commutative rings Formula: see text with identity with certain range of Formula: see text.

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Sarma et al. (Wed,) studied this question.

synapsesocial.com/papers/68e5d251b6db643587568d70 https://doi.org/https://doi.org/10.1142/s0219498825503499

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