Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM = {r E R;rm = 0 V mE M} plays a central
role in our work. In fact, we shall be concemed with the case where annR1i1 = annR(x) for some x EM such modules will be called bounded modules.[t htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful multiplication modules, prime modules and cyclic modules over their endomorphism rings. Also, using boundedness of modules, we showed that :
- The classes of injective modules modulo annihi lator and quasi-injective
modules ru·e equivalent.
- The classes of faithful modules and compactly faithful modules are equi valent.
