On rings with distinguished ideals and their modules.

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dc.contributor.advisor Dugas, Manfred. Buckner, Joshua.
dc.contributor.other Baylor University. Dept. of Mathematics. en 2007-03-01
dc.description.abstract Let S be an integral domain, R an S algebra, and F a family of left ideals of R. Define End(R, F) = {φ ∈ End(R+) : φ(X ) ⊆ X for all X ∈ F }. In 1967, H. Zassenhaus proved that if R is a ring such that R+ is free of finite rank, then there is a left R module M such that R ⊆ M ⊆ QR and End(M+) = R. This motivates the following definitions: Call R a Zassenhaus ring with module M if the conclusion of Zassenhaus' result holds for the ring R and module M . It is easy to see that if R is a Zassenhaus ring then R has a family F of left ideals such that End(R, F) = R. (If F has this property, then call F a Zassenhaus family (of left ideals) of the ring R.) While the converse doesn’t hold in general, this dissertation examines examples of rings R for which the converse does hold, i.e. R has a Zassenhaus family F of left ideals that can be used to construct a left R module M such that R ⊆ M ⊆ QR and End(M+) = R. en
dc.rights Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact for inquiries about permission. en
dc.subject Modules (Algebra). en
dc.subject Abelian groups. en
dc.title On rings with distinguished ideals and their modules. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Worldwide access en
dc.contributor.department Mathematics. en

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