The concept of reduced rank has been a useful tool in studying Noetherian rings, orders in Artinian rings, and rings with Krull dimension. These classes of rings have been generalized, in the commutative setting, to a class of rings called piecewise Noetherian. The purpose of this thesis is to extend this generalization to the noncommutative setting. To that end, a ring with the ascending chain condition on its prime ideals such that every factor ring has finite reduced rank is called a piecewise Noetherian ring.
|Advisor:||Beachy, John A.|
|Commitee:||Blair, William D., Blau, Harvey I., Regev, Alon, Ye, Zhuan|
|School:||Northern Illinois University|
|School Location:||United States -- Illinois|
|Source:||DAI-B 73/05, Dissertation Abstracts International|
|Keywords:||Fully bounded, Noetherian rings, Noncommutative rings, Piecewise, Reduced rank|
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