Tensor products of polynomials


Stephen P. Glasby


Research Report 95-4
Date: 1 June 1994, revised January 1995


This paper defines a binary operation X on the set R[X]* of nonzero polynomials over the integral domain R. The set of polynomials with nonzero constant term is a commutative monoid under X endowed with a natural involution. Let f and g be polynomials over F, the field of fractions of R. We give formulae expressing f X g as a product of irreducible polynomials over F -- a problem which we show is similar to writing the tensor product of simple extensions of F as a direct sum of fields. Finally, we consider questions of unique X-factorization.

AMS Subject Classification (1991)

Primary: 12E05 Secondary: 11T06


The paper is available in the following forms:
TeX dvi format:
tens-prod-pol.dvi.gz (37kB) or tens-prod-pol.dvi (89kB)

tens-prod-pol.ps.gz (82kB) or tens-prod-pol.ps (277kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics