The linear dispersion relation for the magnetorotational instability ( MRI ) is derived including finite Larmor radius ( FLR ) effects .
In particular , the Braginskii form of the ion gyroviscosity , which represents the first-order FLR corrections to the two-fluid equations , is retained .
It is shown that FLR effects are the most important effects in the limit of weak magnetic fields , and are much more important than the Hall effect when \beta _ { i } \gg 1 , where \beta _ { i } is the ratio of the ion thermal pressure to the magnetic pressure .
FLR effects may completely stabilize even MRI modes having wavelengths much greater than the ion Larmor radius .
Some implications for astrophysical accretion disks are discussed .