Abstract :
Let (R, image, k) be a commutative noetherian local ring in which two is a unit. We prove that if J is a five generated grade four perfect ideal in R, then the minimal resolution of R/J by free R-modules is an associative, differential, graded-commutative algebra. This result extends and completes the work in [J. Algebra 159 (1993), 1-46], where the conclusion is shown to hold provided certain technical conditions on Tor are satisfied. The multiplication on the resolution of R/J is constructed using appropriate higher order multiplication on the resolution of R/I, where I is a Gorenstein ideal which is linked to J.
