Let R be an integral domain such that every non-zero quotient R/mR is finite. Consider the unitaries and isometries on \ell^{2}(R) 
 induced by the addition and the multiplication operation of the ring R. The C*-algebra generated by these unitaries and isometries is called
 the ring C*-algebra and was studied by Cuntz and Li. In my talk, I will explain how inverse semigroups can be used to understand these C*-
 algebras. Also some generalisation of the ring C*-algebras will  be discussed.