Abstract
The idea of the composed product of univariate polynomials may be generalized to bivariate polynomials. Using these root-based compositions, we define operations on bivariate polynomials analogous to addition and composition of univariate polynomials. We investigate the seminearring of bivariate polynomials determined by these operations looking at its properties and internal algebraic structures.
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References
Abhyankar, Shreeram, Algebraic Geometry for Scientists and Engineers, American Mathematical Society, Providence, 1990, 89–98.
Ahsan, Javed, Seminearrings characterized by their S-ideals. I. Proc. Japan. Acad., 71, Ser. A. 1995 101–103.
Ahsan, Javed and Zhongkui, Liu, Strongly idempotent seminearrings and their prime ideal spaces. Nearrings, Nearfields, and K-Loops, G Saad and M.J. Thompson eds., Kluwer Academic Publishers, Netherlands, 1997, 151–166.
Gutierrez, Jaime and Ruiz de Velasco, Carlos, Polynomial near-rings in several variables, Near-rings and near-fields (Stellenbosch, 1997), Yuen Fong, Carl Maxson, John Meldrum, Günter Pilz, Andries van der Walt and Leon van Wyk eds., Kluwer Academic Publishers, Dordrecht, 2001, 94–102.
van Hoorn, Willy G. and van Rootselaar, B., Fundamental notions in the theory of seminearrings. Compositio Math., 18, 1967, 65–78.
Mills, Donald and Neuerburg, Kent M., A bivariate analogue to the composed product of polynomials. Algebra Colloquium, 10, 2003, no. 4, 451–460.
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Neuerburg, K.M. (2005). Semi-Nearrings of Bivariate Polynomials over a Field. In: Kiechle, H., Kreuzer, A., Thomsen, M.J. (eds) Nearrings and Nearfields. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3391-5_13
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DOI: https://doi.org/10.1007/1-4020-3391-5_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3390-2
Online ISBN: 978-1-4020-3391-9
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