Goldie dimensions of quotient modules

John Dauns
2001 Journal of the Australian Mathematical Society  
For an infinite cardinal K, an associative ring R is quotient (^-dimensional if the generalized Goldie dimension of all right quotient modules of R R are strictly less than N. This latter quotient property of R/< is characterized in terms of certain essential submodules of cyclic modules being generated by less than K elements, and also in terms of weak injectivity and tightness properties of certain subdirect products of injective modules. The above is the higher cardinal analogue of the known
more » ... theory in the finite K = K o 2000 Mathematics subject classification: 16D50, 16P60.
doi:10.1017/s1446788700002688 fatcat:7np5j2jb6babnpljudjnssxjry