Abstract
Let f and g be two irreducible polynomials of coprime degrees m and n whose zeroes lie in a set . 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).
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