A Note on Semilocal Group Rings
نویسندگان
چکیده
منابع مشابه
On Semilocal Modules and Rings
It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...
متن کاملTits Indices over Semilocal Rings
We present a simplified version of Tits’ proof of the classification of semisimple algebraic groups, which remains valid over semilocal rings. We also provide explicit conditions on anisotropic groups to appear as anisotropic kernels of semisimple groups of a given index.
متن کاملA Note on Isomorphic Commutative Group Algebras over Certain Rings
Suppose G is an abelian group and R is a commutative ring with 1 of char(R) = 0. It is proved that if G is R-favorable torsion and RH and RG are R-isomorphic group algebras for some group H , then H is Rfavorable torsion abelian if and only if either inv(R) = ∅ or inv(R) = ∅ and R is an ND-ring. This strengthens results due to W. Ullery (Comm. Algebra, 1986), (Rocky Mtn. J. Math., 1992) and (Co...
متن کاملA note on decompositions in abelian group rings
We find a necessary and sufficient condition for a normal decomposition of the group of normed units in a commutative group ring (of prime characteristic) into certain its subgroups. This extends a recent assertion of ours in (Vladikavkaz Math. J., 2007). We also give some new proofs of own recent results published in (Miskolc Math. Notes,
متن کاملA note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2002
ISSN: 0011-4642,1572-9141
DOI: 10.1023/b:cmaj.0000027230.45445.09