Bounded Modules - Mahmood, L. S.; Al-Ani, A.S. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
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 -GÂ·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 ruÂ·e equivalent. - The classes of faithful modules and compactly faithful modules are equi valent.