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

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