Abstract
A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitrary commutative ring R, we characterize those polynomials g such that the R-module endomorphism of R[X] given by multiplication by g has a left inverse.
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