Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T00:24:10.688Z Has data issue: false hasContentIssue false
  • English
  • Français

On the tensor product of polynomials over a ring

Part of: Computational aspects and applications

Published online by Cambridge University Press:  09 April 2009

S. P. Glasby
S. P. Glasby
Affiliation:
Department of Mathematics, Central Washington University, WA 98926-7424, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given polynomials a and b over an integral domain R, their tensor product (denoted a ⊗ b) is a polynomial over R of degree deg(a) deg(b) whose roots comprise all products αβ, where α is a root of a, and β is a root of b. This paper considers basic properties of ⊗ including how to factor a ⊗ b into irreducibles factors, and the direct sum decomposition of the ⊗-product of fields.

MSC classification

Secondary: 13P05: Polynomials, factorization
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 307 - 324
Copyright
Copyright © Australian Mathematical Society 2001

References

[BB93]Brawley, J. V. and Brown, D., ‘Composed products and module polynomials over finite fields’, Discrete Math. 117 (1993), 41–56.CrossRefGoogle Scholar
[BC87]Brawley, J. V. and Carlitz, L., ‘Irreducibles and the composed product for polynomials over a finite field’, Discrete Math. 65 (1987), 115–139.CrossRefGoogle Scholar
[G96]Glasby, S. P., ‘Computing in the algebraic closure of a finite field’, Research report 96–14, University of Sydney.Google Scholar
[G95]Glasby, S. P., ‘Tensor products of polynomials’, Research report 95–04, University of Sydney.Google Scholar
[HB82]Huppert, B. and Blackburn, N., Finite groups II (Springer, Berlin, 1982).CrossRefGoogle Scholar
[K73]Knutson, D., λ-rings and the representation theory of the symmetric group, Lecture Notes in Math. 308 (Springer, Berlin, 1973).CrossRefGoogle Scholar
[L80]Lang, S., Algebra (Addison-Wesley, 1980).Google Scholar
[L097]Leedham-Green, C. R. and O'Brien, E. A., ‘Recognising tensor products of matrix groups’, Internal. J. Algebra and Comput. (5) 7 (1997), 541–559.CrossRefGoogle Scholar
[M95]Macdonald, I. G., Symmetric functions and Hall polynomials, 2nd edition (Clarendon, Oxford, 1995).CrossRefGoogle Scholar
[S99]Schwingel, R., ‘The tensor product of polynomials’, Experiment. Math. (4) 8 (1999), 395–397.CrossRefGoogle Scholar