  Let $\goth E(\goth p)$ denote the Eisenstein ideal in the Hecke algebra $\Bbb
T(\goth p)$ of the Drinfeld modular curve $X_0(\goth p)$ parameterizing
Drinfeld modules of rank two over $\Bbb F_q[T]$ of general characteristic with
Hecke level $\goth p$-structure, where $\goth p\triangleleft\Bbb F_q[T]$ is a
non-zero prime ideal. We prove that the characteristic $p$ of the field $\Bbb
F_q$ does not divide the order of the quotient $\Bbb T(\goth p)/\goth E(\goth
p)$ and the Eisenstein ideal $\goth E(\goth p)$ is locally principal.
