ABSTRACT
Let R be an associative algebra and U(R) its group of units. It is in general a difficult problem to relate the structure of U(R) to that of R; for instance, can one understand the effect on R of a group theoretical condition on U(R)? This kind of question in this generality has very little hope to be answered; for instance let A be any ring and R the free associative algebra of rank greater than one over A; it is obvious that in this case U(R) = U(A) and, so, the group of units cannot distinguish between the two rings.
