Max-fully cancellation modules - Nijad Shihab, Dr. Bothaynah; Ali Judi, Heba Mohammad (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
Let R be a commutative ring with identity and let M be a unital an R`-module. We introduce the concept of max-fully cancellation R-module , where an R-module M is called max-fully cancellation if for every nonzero maximal ideal I of R and every two submodules N1And N2, of M such that IN1 =IN2 , implies = N1 and N2 . some characterization of this concept is given and some properties of this concept are proved. The direct sum and the trace of module with max-fully cancellation modules are studied , also the localization of max-fully cancellation module are discussed..