Dissertation/Thesis Abstract

Annihilators and Extensions of Idempotent Generated Ideals
by Heider, Blaise J., Ph.D., University of Louisiana at Lafayette, 2018, 73; 10808908
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Mathematics, Theoretical Mathematics
Keywords: Annihilator, Hull, I-prime, Matrices, Polynomials, cP-Baer
Publication Number: 10808908
ISBN: 9781392041123
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