Left rigid rings

Given any ring R with 1∈R and any family F of left ideals of R, we define for all X∈F}. We call a ring R left rigid if End(R+,Fℓ)=R where Fℓ is the family of all left ideals of R. We will present numerous examples of rings that are left rigid or not left rigid but End(R+,Fℓ) is a left rigid ring.