On diamond products ensuring irreducibility of the associated composed product

İrimağzi C., ÖZBUDAK F.

Communications in Algebra, vol.51, no.7, pp.3134-3142, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.1080/00927872.2023.2178656
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3134-3142
  • Keywords: Composed product, diamond product, irreducible polynomial, permutation polynomial, POLYNOMIALS
  • Middle East Technical University Affiliated: Yes

Abstract

Let f and g be two irreducible polynomials of coprime degrees m and n whose zeroes lie in a set (Formula presented.). Let (Formula presented.) be a diamond product on G. We define the weaker cancelation property of (Formula presented.) and show that it is sufficient to conclude that the composed product of f and g derived from (Formula presented.) is an irreducible polynomial of degree mn. We also prove that a wide class of diamond products on finite fields satisfy the weaker cancelation property. These results extend the corresponding results of Brawley and Carlitz (1987), and Munemasa and Nakamura (2016).