In abstract algebra, the weak dimension of a nonzero right module M over a ring R is the largest number n such that the Tor group
is nonzero for some left R-module N (or infinity if no largest such n exists), and the weak dimension of a left R-module is defined similarly.
The weak dimension was introduced by Henri Cartan and Samuel Eilenberg (1956, p.122).
The weak global dimension of a ring is the largest number n such that
It is at most equal to the left or right global dimension of the ring R.