English

Multiplicities of semidualizing modules

Commutative Algebra 2012-09-04 v2

Abstract

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For certain local Cohen-Macaulay rings (R,m), we verify the equality of Hilbert-Samuel multiplicities e_R(J;C) = e_R(J;R) for all semidualizing R-modules C and all m-primary ideals J. The classes of rings we investigate include those that are determined by ideals defining fat point schemes in projective space or by monomial ideals.

Keywords

Cite

@article{arxiv.1001.2632,
  title  = {Multiplicities of semidualizing modules},
  author = {Susan M. Cooper and Sean Sather-Wagstaff},
  journal= {arXiv preprint arXiv:1001.2632},
  year   = {2012}
}

Comments

12 pages, uses xypic; v.2 has material on enumeration removed. to appear in Comm. Algebra

R2 v1 2026-06-21T14:35:13.777Z