Bound on the a-invariant and reduction numbers of ideals
| dc.creator | D'Cruz, Clare | |
| dc.creator | Kodiyalam, Vijay | |
| dc.creator | Verma, Jugal. K. | |
| dc.date | 2004-04-04 | |
| dc.date.accessioned | 2026-07-07T05:07:05Z | |
| dc.date.available | 2026-07-07T05:07:05Z | |
| dc.description | Let $R$ be a $d$-dimensional standard graded ring over an Artin local ring. Let $M$ be the unique maximal homogeneous ideal of $R.$ Let $h^i(R)_n$ denote the length of $H^i_M(R)_n$, i.e. the nth graded component of the ith local cohomology module of R with respect to M. Define the Eisenbud-Goto invariant of $R$ to be the number $$EG(R)= \sum_{q=0}^{d-1} \binom{d-1}{q} h^q(R)_{1-q}.$$ We prove that the $a$-invariant of $R$ satisfies $$ a(R) \leq e(R)-length(R_1)+(d-1)(length(R_0)-1)+ EG(R).$$ Using this bound we get upper bounds for the reduction number of an $m$-primary ideal of a Cohen-Macaulay local ring $(R,m)$ whose associated graded ring $G(m)$ has almost maximal depth. | |
| dc.description | 8 pages. to appear in Journal of algebra 274(2004) 594-601 | |
| dc.identifier | https://arxiv.org/abs/math/0404066 | |
| dc.identifier | http://arxiv.org/abs/math/0404066 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70718 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D45 14B15 | |
| dc.title | Bound on the a-invariant and reduction numbers of ideals | |
| dc.type | text |