On duo-max modules

The paper’s goal is to examine the Max-ring concept in the present. To achieve our aim, we’ll employ a novel notion called a dual module. Greater than the duo module provided by Ozcan and Harmanci is the duo-max-module. We established that a duo-maximal again max-module, Rduo Max-ring, has a direct summand. Also, R is the maximum ring if every module M over R is semi-primitive. We looked at N as the maximum of the max-injective module and R as the duo-max ring. On the other hand, any nonzero element of M has an annihilator that is semimax. Ideally, M is a semi- duo-maximal module, and R is max-ring module. Finally, a number of definitions, attributes, and fresh findings have been presented together with some links between these types of Max-rings.