modules over group rings of groups with restrictions on the system of all proper subgroups
نویسندگان
چکیده
we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we study the cases: 1) $mathfrak m$ is the class of all artinian $bf r$--modules, $bf r$ is either the ring of integers or the ring of $p$--adic integers; 2) $mathfrak m$ is the class of all finite $bf r$--modules, $bf r$ is an associative ring; 3) $mathfrak m$ is the class of all finite $bf r$--modules, $bf r$$=f$ is a finite field.
منابع مشابه
on one class of modules over group rings with finiteness restrictions
the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring, a group $g$ has infinite section $p$-rank (or infinite 0-rank), $c_{g}(a)=1$, and for every proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is a finite $bf r$-module. it is proved that if the group $g$ under consideration is local...
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عنوان ژورنال:
international journal of group theoryجلد ۴، شماره ۴، صفحات ۴۳-۴۸
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