  This paper presents the right-left symmetry of the CS and max-min CS
conditions on nonsingular rings, and generalization to nonsingular modules. We
prove that a ring is right nonsingular right CS and left Utumi if and only if
it is left nonsingular left CS and right Utumi. A nonsingular Utumi ring is
right max (resp. right min, right max-min) CS if and only if it is left min
(resp. left max, left max-min) CS. In addition, a semiprime nonsingular ring is
right max-min CS with finite right uniform dimension if and only if it is left
max-min CS with finite left uniform dimension.
