The probability that the multiplication of two ring elements is zero

Author:

Esmkhani M. A.1,Jafarian Amiri S. M.1

Affiliation:

1. Department of Mathematics, Faculty of Sciences, University of Zanjan, P. O. Box 45371-38791, Zanjan, Iran

Abstract

Let [Formula: see text] be a finite commutative ring. We denote by [Formula: see text] the probability that the multiplication of two randomly chosen elements of [Formula: see text] is zero. In this paper, we show that either [Formula: see text] or [Formula: see text] for any ring [Formula: see text] and determine all rings [Formula: see text] with [Formula: see text]. Also, we obtain the structures of rings [Formula: see text] having maximum or minimum value of [Formula: see text] among all rings with identity of the same size. We characterize all rings [Formula: see text] with identity such that [Formula: see text]. Finally, we compute [Formula: see text] where [Formula: see text] is a PIR local ring.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The probability that the product of three elements in a finite ring is zero;Journal of Algebra and Its Applications;2024-08-07

2. THE PROBABILITY OF ZERO MULTIPLICATION IN FINITE GROUP ALGEBRAS;INT J GROUP THEORY;2024

3. Commuting and product-zero probability in finite rings;International Journal of Algebra and Computation;2024-02-20

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