Abstract
In the paper Don Blackett presented at the 1993 Fredericton Near-ring conference he showed some applications of seminearring theory to probability generating functions. It turns out that his main result can be extended to show that all polynomials over a commutative semifield with zero (for instance the non-negative rationals) can be decomposed via composition and multiplication to affine polynomials, in fact to a special class of affine polynomials.
Suported by Contained Project “Jo” and KIP Stipendium 1994
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. F. Birkenmeier, H. E. Heatherly, and G. Pilz. Near-rings and rings generated by homo-morphisms on groups. This volume.
D. W. Blackett. Connecting seminearrings to probability generating functions. In: Near-Rings and Near-Fields, Y. Fong et al. (eds.), Kluwer Academic Publishers, Dordrecht, 75–82, 1995.
D. B. Benson and J. Tiuryn. Fixed points in free process algebras with silent events, part I. Technical Report CS-86–152, Computer Science Dept, Washington State University, 1986.
J. C. M. Baeten and W. P. Weijland. Process Algebra, volume 18 of Cambridge Tracts in Computer Science. Cambridge University Press, 1990.
A. M. W. Glass and W. C. Holland. Lattice-Ordered Groups. Kluwer Academic Publishers, Dordrecht, 1989.
H. C. Hutchins and H. J. Weinert. Homomorphisms and kernels of semifields. Period. Math. Hung. 21, 113–152, 1990.
U. Hebisch and H. J. Weinert. Halbringe: Algebraische Theorie und Anwendungen in der Informatik. Teubner, Stuttgart, 1993.
H. Lausch and W. Nöbauer. Algebra of Polynomials. North-Holland, Amsterdam, 1973.
D. McLean. Idempotent semigroups. American Math. Monthly 64, 110–113, 1954.
G. Pilz. Near-rings. North-Holland, Amsterdam, 2. ed., 1983.
H. J. Weinert. Zur Theorie der Halbfastkörper. Stud. Sci. Math. Hung. 16, 201–218, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Kluwer Academic Publishers
About this chapter
Cite this chapter
Boykett, T. (1997). Seminearrings of Polynomials Over Semifields: A Note on Blackett’s Fredericton Paper. In: Saad, G., Thomsen, M.J. (eds) Nearrings, Nearfields and K-Loops. Mathematics and Its Applications, vol 426. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1481-0_14
Download citation
DOI: https://doi.org/10.1007/978-94-009-1481-0_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7163-5
Online ISBN: 978-94-009-1481-0
eBook Packages: Springer Book Archive