On modules over group rings of nilpotent groups
We study an $\mathbf{R}G$-module $A$, where $\mathbf{R}$ is a ring, $A/C_A(G)$ is not a minimax $\mathbf{R}$-module, $C_A(G) = 1$, and $G$ is a nilpotent group. Let $\mathfrak{L}_{nm}(G)$ be the system of all subgroups $H \leq G$ such that the quotient modules $A/C_A(G)$ are not minimax $\mathbf{R}...
Saved in:
| Date: | 2012 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2552 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study an $\mathbf{R}G$-module $A$, where $\mathbf{R}$ is a ring, $A/C_A(G)$ is not a minimax $\mathbf{R}$-module, $C_A(G) = 1$, and $G$ is a nilpotent group.
Let $\mathfrak{L}_{nm}(G)$ be the system of all subgroups $H \leq G$ such that the quotient modules $A/C_A(G)$ are not minimax $\mathbf{R}$-modules.
We investigate a $\mathbf{R}G$ - module $A$ such that $\mathfrak{L}_{nm}(G)$ satisfies either the weak minimal condition or the weak maximal condition as an ordered set.
It is proved that a nilpotent group $G$ that satisfies these conditions is a minimax group. |
|---|