Ansari, Mohammad Rashid Kamal (1994) COTORSION MODULES OVER ORE DOMAINS. PhD thesis, University of Karachi, Karachi.
Matlis  has discussed cotorsion modules over integral domains whereas Henderson and orzech  has discussed cotorsion modules over commutative rings. In this thesis we emphasize non-commutative 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 D-cotorsion modules. Our results regarding the connection between D-cotorsion modules and modules appearing as Ext (A,B) generalize the results of matlis , Henderson and Orzech , Diana Yun-Dee Wei  and Qureshi . Moreover, we generalize the work of matlis  regarding the links of torsion-cotorsion duality and cotorsion-cotorsion free duality with A-A* duality. Besides this we study the cotorsion completion functors of matlis  in the non-commutative 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 oreÃÂÃÂÃÂÃÂ² domains also. In additions, a characterization of left ore domain in terms of cotorsion modules is provided.
|Item Type:||Thesis (PhD)|
|Uncontrolled Keywords:||cotorsion modules, ore domains, associative rings, left ore domains, torsion modules, torsion free modules, divisible modules, i-functors, d-rich functors|
|Subjects:||Physical Sciences (f) > Mathematics(f5)|
|Deposited By:||Mr. Muhammad Asif|
|Deposited On:||27 Oct 2006|
|Last Modified:||04 Oct 2007 21:03|
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