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On coprimeness of two polynomials in the framework of conjugate product

On coprimeness of two polynomials in the framework of conjugate product

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The right and left con-Sylvester matrices for two polynomials are defined, and then the criteria for right and left coprimeness of two polynomials in the framework of conjugate product are given in terms of the determinant of the right and left con-Sylvester matrices, respectively. The results in this study can be viewed as a generalisation of the well-known Sylvester resultant criterion for coprimeness of two polynomials in the framework of ordinary product.

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