Non-noetherian groups and primitivity of group rings of their groups
Project/Area Number |
26400055
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Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | University of Hyogo (2015-2016) Okayama Shoka University (2014) |
Principal Investigator |
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 群環の原始性 / 非ネーター群 / 無限群 / グラフ理論 / 半原始問題 / 1関係子群 / 群の融合積 / HNN拡大群 / 局所自由群 / 無限群の群環 / 原始性 / 半原始性 / HNN拡大 / 1関係子群 |
Outline of Final Research Achievements |
A ring R is said to be (right) primitive if it contains a faithful irreducible (right) R-module, which is a generalization of a simple ring. A typical example of primitive ring which is not simple is the ring consists of liner transformations on an infinite dimensional vector space. The main purpose of this work was to determine, as generally as possible, for which fields K the group algebra KG of a non-noetherian group G is primitive. To do this, we constructed what we call an SR-graph theory, and apply this to proving primitivity of group algebras of non-noetherian groups; the problem can be reduced to find an SR-cycle in a given SR-graph. In fact, by making use of the method, we could show primitivity of group algebras of groups which belong to many classes of non-noetherian groups, including free groups, locally free groups, free products, amalgamated free products, HNN-extensions and one relator groups.
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Report
(4 results)
Research Products
(25 results)