Dissertation/Thesis Abstract

Noncommutative piecewise Noetherian rings
by Pearson, Abigail C., Ph.D., Northern Illinois University, 2011, 92; 3494399
Abstract (Summary)

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.

Indexing (document details)
Advisor: Beachy, John A.
Commitee: Blair, William D., Blau, Harvey I., Regev, Alon, Ye, Zhuan
School: Northern Illinois University
Department: Mathematical Sciences
School Location: United States -- Illinois
Source: DAI-B 73/05, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Fully bounded, Noetherian rings, Noncommutative rings, Piecewise, Reduced rank
Publication Number: 3494399
ISBN: 9781267160324
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