Equivalent presentations of modules over Prüfer domains

http://dx.doi.org/10.4153/CMB-1998-024-6
Canad. Math. Bull. 41(1998), 151-157

  Published:1998-06-01
 Printed: Jun 1998

If $F$ and $F^\prime$ are free $R$-modules, then $M \cong F/H$ and $M \cong F^\prime/H^\prime$ are viewed as equivalent presentations of the $R$-module $M$ if there is an isomorphism $F \to F^\prime$ which carries the submodule $H$ onto $H^\prime$. We study when presentations of modules of projective dimension $1$ over Pr\"ufer domains of finite character are necessarily equivalent.