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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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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.