DIGRAPHS FOR COMMUTATIVE RINGS WITH MULTIPLICATIVE (GENERALIZED)-DERIVATIONS

Algebraic structures such as semigroup, group, rings, field, modules play a prominent role in Mathematics with wide range of applications in different fields of human endeavors. The commutativity theorems in their general form require the structure theory for noncommutative rings. We examined several results dealing with conditions under which ring is commutative and such conditions are placed on the ring itself or its subsets, or its commutators. The concept of digraphs in commutative rings has been applied to justify our results on commutativity theorems with multiplicative (generalized) derivations.