dc.contributor.author |
Gebai, Ryma Ismail. |
dc.date.accessioned |
2013-10-02T09:23:25Z |
dc.date.available |
2013-10-02T09:23:25Z |
dc.date.issued |
2013 |
dc.identifier.uri |
http://hdl.handle.net/10938/9641 |
dc.description |
Thesis (M.S.)--American University of Beirut, Department of Mathematics, 2012. |
dc.description |
Advisor : Dr. Abu Khuzam, Hazar, Professor, Mathematics--Committee Members : Dr. Nahlus Nazih, Professor, Mathematics ; Dr. El Khoury Sabine, Assistant Professor, Mathematics. |
dc.description |
Includes bibliographical references (leaves 47-48) |
dc.description.abstract |
Finiteness conditions on a ring or on certain subsets of a ring have several implications on the structure of the ring. This study of finiteness conditions was motivated by a well-known theorem of Wedderburn which states that a finite division ring must be a field. In one of our results in this study, we prove that a finite ring which is multiplicatively generated by idempotent elements must be Boolean. We also study the structure of rings having at most finitely many nonnilpotent elements. Indeed, we prove that a ring having at most finitely many nonnilpotent elements must be either nil or finite. We also show that a ring with a finite number of non-central elements is either finite or commutative. Since every finite ring is clearly periodic, we consider a more general class of the above rings, which are rings satisfying the property that for each x∊R , either x is periodic or there exists a positive integer K=K(x) such that x(to the power k) ∊C (where C is the center of R ) for all k≥K. We study the structure of certain classes of these rings. In particular, we show that a prime ring satisfying the above property is either commutative or periodic. |
dc.format.extent |
vii, 48 leaves : ill. ; 30cm. |
dc.language.iso |
eng |
dc.relation.ispartof |
Theses, Dissertations, and Projects |
dc.subject.classification |
T:005796 AUBNO |
dc.subject.lcsh |
Rings (Algebra) |
dc.subject.lcsh |
Noncommutative rings. |
dc.title |
Rings with finiteness conditions on certain subsets |
dc.type |
Thesis |
dc.contributor.department |
American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics. |