Idempotents in group rings
| dc.contributor.author | Marciniak, Zbigniew | en |
| dc.contributor.committeechair | Farkas, Daniel R. | en |
| dc.contributor.committeemember | Green, E.L. | en |
| dc.contributor.committeemember | Dickman, R.F., Jr. | en |
| dc.contributor.committeemember | Feustel, Charles D. | en |
| dc.contributor.committeemember | Hannsgen, Kenneth B. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2017-11-09T21:42:07Z | en |
| dc.date.available | 2017-11-09T21:42:07Z | en |
| dc.date.issued | 1982 | en |
| dc.description.abstract | The von Neumann finiteness problem for k[G] is still open. Kaplansky proved it in characteristic zero. He used the nonvanishing of the trace: tr(e) = 0 implies e = 0 for any idempotent e ∊ k[G]. Assume now that char k = p > 0. Now tr can vanish on nonzero idempotents. Instead, we study the lifted trace ltr. For e = e² ∊ k[G], define ltr(e) by ê(1) where ê = Σ{x ∊ G}ê(x)x lifts e. Here ê is an infinite series with |ê(x)|<sub>p</sub>→0, where each ê(x) lives in the Witt vector ring of k. We prove that ltr(e) depends on e only, it is a p-adic integer and ltr(e) = ltr(f) if f is equivalent to e. Also ltr(e) ∊ Q and ltr(e) = 0 implies e = 0 if G is polycyclic-by-finite. We conjecture that -log<sub>p</sub>|ltr(e)|<sub>p</sub> < |supp(e)|. We prove this for e central and for e = e² ∊ k[G] with |G| ≤ 30. In the last section, we give the example of an idempotent e such ath supp(f) is infinite for all f ~ e. Finally we estimate |<supp(e)>| for central idempotents e. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | v, 85, [1] leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/80271 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute and State University | en |
| dc.relation.isformatof | OCLC# 9008469 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1982.M372 | en |
| dc.subject.lcsh | Group rings | en |
| dc.title | Idempotents in group rings | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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