In this scientific paper we dealt with three different types of
homomorphisms between two given ideals in a ring with unity shown as
follows: ring homomorphism, R- module homomorphism and ideal
homomorphism, which were supported by several example
s.
Furthermore, we prove that the family of ideals in a ring R with ring, R -
module and ideal homomorphisms forms the category of ideals of the first,
second and third type, respectively. The next step was dedicated to support all
previous ideals by examples and functor between such categories.
