R is a regular local ring of dimension $d$, and $I$ an ideal. If $R/I$ has depth $d − 1$, then $I$ is principal.

Question

is this true?

$R$ is a regular local ring of dimension $d$, and $I$ an ideal. If $R/I$ has depth $d − 1$, then $I$ is principal.

if it is true please help me by a hint

Do you mean $R/I$ has depth $d-1$? – Brian Fitzpatrick May 13 '14 at 02:01 — Brian Fitzpatrick, May 13 '14 at 02:01

score 3 · Accepted Answer · answered May 13 '14 at 02:51

3

answered May 13 '14 at 02:51

Matt E

1 Answers1