On diamond products ensuring irreducibility of the associated composed product

Date

2023-2-16

Author

İrimağzi, Canberk
Özbudak, Ferruh

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Let f and g be two irreducible polynomials of coprime degrees m and n whose zeroes lie in a set G⊆F¯¯¯q . Let ⋄ be a diamond product on G. We define the weaker cancelation property of ⋄ and show that it is sufficient to conclude that the composed product of f and g derived from ⋄ 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).

Subject Keywords

Algebra and Number Theory, Finite fields

URI

https://www.tandfonline.com/doi/ref/10.1080/00927872.2023.2178656?scroll=top&role=tab
https://hdl.handle.net/11511/102078

Journal

Communications in Algebra

DOI

https://doi.org/10.1080/00927872.2023.2178656

Collections

Department of Mathematics, Article

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Citation Formats

C. İrimağzi and F. Özbudak, “On diamond products ensuring irreducibility of the associated composed product,” Communications in Algebra, pp. 1–9, 2023, Accessed: 00, 2023. [Online]. Available: https://www.tandfonline.com/doi/ref/10.1080/00927872.2023.2178656?scroll=top&role=tab.