### Article

Kyungpook Mathematical Journal 2022; 62(3): 437-453

**Published online** September 30, 2022

Copyright © Kyungpook Mathematical Journal.

### An Alternative Perspective of Near-rings of Polynomials and Power series

Fatemeh Shokuhifar, Ebrahim Hashemi∗ and Abdollah Alhevaz

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 316-3619995161, Iran

e-mail : shokuhi.135@gmail.com, eb_hashemi@yahoo.com or eb_hashemi@shahroodut.ac.ir and a.alhevaz@gmail.com or a.alhevaz@shahroodut.ac.ir

**Received**: June 26, 2021; **Revised**: January 2, 2022; **Accepted**: January 13, 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let

**Keywords**: Near-ring of polynomials, Zero-divisor graph, Compressed zero-divisor graph, Diameter of graph, Near-ring of formal power series