Lately I remembered an exercise from an algebra class from Jacobson's book: Prove that if an element has more than one right inverse then it has infinitely many, Jacobson attributes this excercise to Kaplansky. Regardless of the solution I began to wonder:
Does anybody know any explicit examples of rings that have this property of having elements with infinitely many (or, thanks to Kaplansky, multiple) right inverses? Is the same true for left inverses? I came across an article from the AMS Bulletin that studied this topic but skimming through it I could not find an explicit example, sorry I cant remember the author. Anyways, thanks and good luck!