On Distinguishing Local Finite Rings from Finite Rings Only by Counting Elements and Zero Divisors

Authors

  • Marcos José González Departamento de Matemáticas Universidad Simón Bolívar Apartado Postal 89000 Caracas 1080-A Venezuela

Keywords:

Finite ring, Zero-divisor, Local rings

Abstract

Thepurposeof this shortcommunication is to prove thefollowing: {\emLet$R$ be a finite associativeringwith unit. Then$R$ is local if and only if $|R| = p^n$ and $|Z(R)| = p^m$for some prime number$p$ and integers$1\leq m <n$}.  Forthecommutative case, this havebeenrecentlydiscovered byBehboodi and Beyranvand\cite[Theorem~3]{bb}. Wewill also presentyetanother proof for thecommutative case.

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Published

2014-01-29

Issue

Vol. 7 No. 1: (January 2014)

Section

Mathematical and Fuzzy Logic

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How to Cite

On Distinguishing Local Finite Rings from Finite Rings Only by Counting Elements and Zero Divisors. (2014). European Journal of Pure and Applied Mathematics, 7(1), 109-113. https://www.ejpam.com/index.php/ejpam/article/view/1802