Bounded modules

Abstract EN

I.el م be a commutative ring with identity, and let M be a unitary (let!) R-module.

The ideal arm ft M = {٢ € R\rm = 0 V m £ M} plays a central our work.

In faet, we shall be concerned with the ease wrhcre annftM = anti ft (x) for some such modules will be called bounded modules.lt t،im$ out that there are many classes of modules properly contained in the class ()!'bounded modules such as cyclic modules, torsion-free modules,faithful multiplication modules, prime modules and cyclic modules over their endomorphism rin§s.

Also, using boundedness of modules, we showed that : The classes of injective modules modulo annihilator and quasi-injective modules arc e؟uivalent.

The classes of faithful modules and compactly faithful modules are equivalent■