Cyclic Modules over End(VD ) Whose Endomorphism Ring Is an Ultrapower of D

Let V_D be an infinite dimensional right vector space and put R = End(V_D ). If B is a basis of V, to each free ultrafilter A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187605/d46d5034-f914-41b4-a96f-9f0731bff786/content/eq2638.tif"/> on B is associated a left ideal M of R. It is proved that the endomorphism ring End _R (R/M) of the left cyclic R-module R/M is isomorphic to the ultraproduct D^B / A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187605/d46d5034-f914-41b4-a96f-9f0731bff786/content/eq2639.tif"/> .