Multiplicities and a dimension inequality for unmixed modules
| dc.creator | Sather-Wagstaff, Sean | |
| dc.date | 2002-12-09 | |
| dc.date.accessioned | 2026-07-07T04:53:37Z | |
| dc.date.available | 2026-07-07T04:53:37Z | |
| dc.description | We prove the following result, which is motivated by the recent work of Kurano and Roberts on Serre's positivity conjecture. Assume that (R,m) is a local ring with finitely-generated module M such that R/ann(M) is quasi-unmixed and contains a field, and that p and q are prime ideals in the support of M such that p is analytically unramified, p+q is m-primary and e(M_p)=e(M). Then dim(R/p)+dim(R/q)\leq dim(M). We also prove a similar theorem in a special case of mixed characteristic. Finally, we provide several examples to explain our assumptions as well as an example of a noncatenary, local domain R with prime ideal p such that e(R_p)>e(R)=1. | |
| dc.identifier | https://arxiv.org/abs/math/0212107 | |
| dc.identifier | http://arxiv.org/abs/math/0212107 | |
| dc.identifier | Journal of Algebra 238 (2001), 372-388, doi:10.1006/jabr.2000.8630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65919 | |
| dc.subject | Commutative Algebra | |
| dc.title | Multiplicities and a dimension inequality for unmixed modules | |
| dc.type | text |