Local Limitations of the Ext Functor Do Not Exist

In this note it is shown that for k a field, and for the four-dimensionalalgebra = kx, y/x², y², xy + qyx when qⁿ 1, 0 for all n, thereexist a two-dimensional module M and a family of two-dimensionalmodules M_i, i = 1, 2, ..., such that for i equal to 0, j and j + 1, and otherwise. This is probably the most straightforward examplegiving a negative answer to a question raised by Maurice Auslander.2000 Mathematics Subject Classification 16D10, 16E10, 16E30,16G10, 16G20.