One of the first systems developed to provide online security is what is now known as RSA encryption. This method has been first published by Rivest, Shamir and Adleman in 1978. Even on this day, a modification of the first method of RSA encryption is being used and considered safe. This paper explores a number of mathematical structures and describes whether or not it could be possible to extend RSA encryption. In this paper we will focus on verifying whether the RSA encryption and decryption algorithms are well defined on the mathematical structures.