With PQDT Open, you can read the full text of open access dissertations and theses free of charge.
About PQDT Open
Search
We define a ring R to be right cP- Baer if the right annihilator of a cyclic projective right R-module is generated by an idempotent. We also define a ring R to be right I-extending if each ideal generated by an idempotent is right essential in a direct summand of R. It is shown that the two conditions are equivalent in a semiprime ring. Next we define a right I-prime ring, which generalizes the prime condition. This condition is equivalent to all cyclic projective right R-modules being faithful. For a semiprime ring, we show the existence of a cP -Baer hull. We also provide some results about the p.q.-Baer hull and when it is equal to the cP-Baer hull. Polynomial and formal power series rings are studied with respect to the right cP-Baer condition. In general, a formal power series ring over one indeterminate in which its base ring is right p.q.-Baer ring is not necessarily right p.q.-Baer. However, if the base ring is right cP-Baer then the formal power series ring over one indeterminate is right cP-Baer. The fifth chapter is devoted to matrix extensions of right cP-Baer rings. A characterization of when a 2-by-2 generalized upper triangular matrix ring is right cP-Baer is given. The last major theorem is a decomposition of a cP-Baer ring, satisfying a finiteness condition, into a generalized triangular matrix ring with right I-prime rings down the main diagonal. Examples illustrating and delimiting our results are provided.
Advisor: | Birkenmeier, Gary F. |
Commitee: | Heatherly, Henry E., Lynd, Justin, Magidin, Arturo |
School: | University of Louisiana at Lafayette |
Department: | Sciences |
School Location: | United States -- Louisiana |
Source: | DAI-B 80/08(E), Dissertation Abstracts International |
Source Type: | DISSERTATION |
Subjects: | Mathematics, Theoretical Mathematics |
Keywords: | Annihilator, Hull, I-prime, Matrices, Polynomials, cP-Baer |
Publication Number: | 10808908 |
ISBN: | 978-1-392-04112-3 |