Computing Gorenstein Colength
| dc.creator | Ananthnarayan, H. | |
| dc.date | 2008-10-24 | |
| dc.date.accessioned | 2026-07-07T10:13:13Z | |
| dc.date.available | 2026-07-07T10:13:13Z | |
| dc.description | Given an Artinian local ring $R$, we define its Gorenstein colength $g(R)$ to measure how closely we can approximate $R$ by a Gorenstein Artin local ring. In this paper, we show that $R = T/I$ satisfies the inequality $g(R) \leq λ(R/\soc(R))$ in the following two cases: (a) $T$ is a power series ring over a field of characteristic zero and $I$ an ideal that is the power of a system of parameters or (b) $T$ is a 2-dimensional regular local ring with infinite residue field and $I$ is primary to the maximal ideal of $T$. In the first case, we compute $g(R)$ by constructing a Gorenstein Artin local ring mapping onto $R$. We further use this construction to show that an ideal that is the $n$th power of a system of parameters is directly linked to the $(n-1)$st power via Gorenstein ideals. A similar method shows that such ideals are also directly linked to themselves via Gorenstein ideals. Keywords: Gorenstein colength; Gorenstein linkage. | |
| dc.identifier | https://arxiv.org/abs/0810.4542 | |
| dc.identifier | http://arxiv.org/abs/0810.4542 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172452 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Computing Gorenstein Colength | |
| dc.type | text |