Thursday, February 26th, 11:00-12:00

A divisibility test of Arend Heyting, for polynomials over a field in an intuitionist 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.