# Tensor products of polynomials

## Author

**Stephen P. Glasby**

## Status

Research Report 95-4

Date: 1 June 1994, revised January 1995

## Abstract

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

## Content

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

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

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Sydney Mathematics and Statistics