Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If $A$ is an integral domain and $I$ is an ideal of $A$ generated by a regular sequence $f_1,\ldots,f_r$. Is $I$ flat (as an $A$-module)?

share|improve this question
    
Is $A$ Noetherian? –  shamovic Apr 18 '11 at 12:22
add comment

1 Answer 1

up vote 3 down vote accepted

No, the ideal I needn't be flat. Consider the polynomial ring $k[X,Y]$ in two indeterminates over the field $k$. The ideal $I=(X,Y)$ is generated by the regular sequence $X,Y$ but it is not flat. Indeed, since I is finitely presented, it would be projective, of rank 1 hence free : the ideal $I$ would then be principal, which it is not.

share|improve this answer
2  
Perfect. Thanks! –  Bonanza Apr 18 '11 at 16:16
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.