فئة المثاليات في حلقة R

Abstract EN

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 examples.

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.

Finally, using the properties of ideals we prove that for two isomorphic rings R = S then I3R, the category of ideals in /?of the third type is isomorphic with I3R , moreover I3R*5 = I3R* I3S