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Title:	Some generalisations of supplemented module related to length property
Authors:	Majid Mohammed Abed Al-Shughairy (P64711)
Supervisor:	Abd Ghafur Ahmad, Prof. Madya Dr.
Keywords:	Supplemented module Radical modules Finite length property Dissertations, Academic -- Malaysia
Issue Date:	10-Jan-2015
Description:	The main objective of this research is to generalise up the highest order of generalization of supplemented modules by establishing new conditions on these modules. Due to the relations between radical modules and generalisation of supplemented modules, a notion of rad-supplemented module is introduced. There are two properties in this generalisation. These two properties are rad-supplemented and finite hollow dimension it is necessary for radical module to be equal to while the length of any module is represented by finite hollow dimension. The main examples of the first generalization introduced are amply supplemented module, D11-module, weakly supplemented module and principally supplemented module. Examples for the second generalization of supplemented module are strongly-D11-module, completely-D11-module, Rad-D11-module, finitely weakly supplemented module and weak-D11-module. The main examples for the third generalisation introduced are _-completely-D11-module, completely-Rad-D11-module and finitely-weak-Rad-supplemented module. Then, the relationship between these generalisations and finite length property are determined. The modules for these relations identified are semisimple, simple and hollow dimension modules. One of the goals is to reach up the highest order for the generalisation of supplemented module by using newly introduced conditions. There is a relationship between Artinian and Noetherian modules with finite length property. Therefore a concept of hollow dimension is one of many ideas in finite length property. we can say not all the generalisations have relationship with length of the module. This fills the gap since most researcher do concentrate only on generalisation finite length properties. ,Ph.D.
Pages:	140
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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