Some Classification Theorems and Endomorphisms in New Classes

Let ℧ be a prime ring of char(℧) not equal 2 with its center Z. This article introduces new classes of endomorphisms and investigates how they relate to antiautomorphisms of prime rings and the commutativity of prime rings. Additionally, we fully describe and classify some of these endomorphisms. We also give examples to prove the necessity of the numerous restrictions included in the hypotheses of our results.