

Title of Thesis
COTORSION MODULES OVER ORE DOMAINS 
Author(s)
Mohammad Rashid Kamal Ansari 
Institute/University/Department Details
Department of Mathematics/ University of Karachi 
Session
1994 
Subject
Mathematics 
Number of Pages
115 
Keywords (Extracted from title, table of contents and abstract of thesis)
cotorsion modules, ore domains, associative rings, left ore domains, torsion modules, torsion free modules, divisible modules, ifunctors, drich functors 
Abstract Matlis [16] has discussed cotorsion modules over integral domains whereas Henderson and orzech [12] has discussed cotorsion modules over commutative rings. In this thesis we emphasize noncommutative situations. We study cotorsion modules over associative rings and give particular attention to cotorsion modules over ore domains. With reference to an arbitrary ring R which is embedded in a ring D, we introduce Dcotorsion modules. Our results regarding the connection between Dcotorsion modules and modules appearing as Ext (A,B) generalize the results of matlis [16], Henderson and Orzech [12], Diana YunDee Wei [30] and Qureshi [23]. Moreover, we generalize the work of matlis [16] regarding the links of torsioncotorsion duality and cotorsioncotorsion free duality with AA* duality. Besides this we study the cotorsion completion functors of matlis [16] in the noncommutative case. Furthermore, we show that the category of cotorsion modules, which is a category with kernels and cokernels in case of integral domains, is a category with kernels and cokernels and cokernels in case of two sided oreÎ˛ domains also. In additions, a characterization of left ore domain in terms of cotorsion modules is provided.






S. No. 
Chapter 
Title of the Chapters 
Page 
Size (KB) 





1 
0 
Contents 

135.03 KB 





2 
1 
Introduction 
1 
196.24 KB 

1.1 
Preliminaries 
11 

1.2 
Left Ore Domains 
11 

1.3 
Dual Modules 
12 

1.4 
Torsion, Torsion Free And Divisible Modules 
20 

1.5 
Exact Sequences Of Matlis 
34 





3 
2 
DTorsion And D Cotorsion Modules 
41 
111.67 KB 

2.1 
DTorsion Modules 
41 

2.2 
DCotorsion Modules 
45 





4 
3 
Cotorsion Modules Over Ore Domains 
58 
203.86 KB 

3.1 
Homomorphic Image Of A Torsion Free And Divisible 
58 

3.2 
Cotorsion Modules 
67 

3.3 
Cotorsion Free Modules 
72 

3.4 
Characterization Of Left Ore Domain 
84 





5 
4 
IFunctors And DRich Functors 
89 
179.93 KB 

4.1 
Definitions And Examples 
89 

4.2 
Natural Transformation Of IFunctors 
95 

4.3 
References 
112 





