2014/07/01 by Sankar P. Dutta, Dutta, Sankar P.
Mathematics · #13D22 #13D25 #13H05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D02 #Secondary 13C15 #math.AC #msc:13C15 #msc:13D02 #msc:13D22 #msc:13D25 #msc:13H05
paper · pdf · doi:10.48550/arxiv.1407.0096
arxiv created 2014/07/01 · arxiv updated 2014/07/02
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular we derive that in any local ring R of mixed characteristic p > 0, where p is a non-zero-divisor, if I is an ideal of finite projective dimension over R and p is in I or p is a non-zero-divisor on R/I, then every minimal generator of I is a non-zero-divisor. Hence if P is a prime ideal of finite projective dimension in a local ring R, then every minimal generator of P is a non-zero-divisor in R.