Recall that in a commutative ring $A$ an ordered pair of elements (a,b) is said to form a regular sequence if the ideal $\langle a,b\rangle $ is strictly included in $A$ ,if $a$ is not a zero-divisor in $A$ and if the class of $b$ is not a zero-divisor of $A/\langle a\rangle$.

A friend of mine has asked me if in that case we can conclude that $\langle b,a\rangle $ is also a regular sequence *under the assumption that $A$ is a noetherian domain*.

The answer is known to be yes for a *local* noetherian ring $A$, even it is not a domain

[Since I couldn't answer his question, I suggested to my friend that he ask here but he prefers that I do that]