A bivariate analogue to the composed product of polynomials

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The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in particular, the Puiseux expansion) of bivariate polynomials, we generalize the univariate results. We define a bivariate composed sum, composed multiplication, and composed product (based on function composition). Further, we investigate the algebraic structure of certain classes of bivariate polynomials under these operations. We also generalize a result of Brawley and Carlitz concerning the decomposition of polynomials into irreducibles.
10 pages; to appear in Algebra Colloquium

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Rings and Algebras, 12Y05; 13P99

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http://salesiana.dossiersoluciones.com/handle/123456789/69458

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312093
 http://arxiv.org/abs/math/0312093

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arXiv