Goldie dimensions of quotient modules

For an infinite cardinal N, an associative ring R is quotient N-<-dimension al if the generalized Goldie dimension of all right quotient modules of R-R are strictly less than N. This latter quotient property of R-R is characte rized in terms of certain essential submodules of cyclic modules being gene rated by less than R elements, and also in terms of weak injectivity and ti ghtness properties of certain subdirect products of injective modules. The above is the higher cardinal analogue of the known theory in the finite N = N-0 case.