Abstract
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..
Highlights
Throughout this thesis all rings are commutative rings with unity and all modules are unital modules
In section One, we introduce the definition of max-fully cancellation module and we give some characterizations for a module to be max-fully cancellation module, see proposition(1.7), many propositions and results related with this concept are given
We study the direct sum of max-fully cancellation modules and many of important results are given, see proposition (2.2), proposition(2.7) and proposition(2.8)
Summary
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 submodulesN1 andN2 , of M such that IN1=IN2 , implies N1 = 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 , the localization of max-fully cancellation module are discussed
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