Semilocal Group Rings in Characteristic Zero
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...
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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.
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The study of zero-divisors in group rings had become interesting problem since 1940 with the famous zero-divisor conjecture proposed by G.Higman [2]. Since then several researchers [1, 2, 3] have given partial solutions to this conjecture. Till date the problem remains unsolved. Now we introduce the notions of Smarandache zero divisors (S-zero divisors) and Smarandache week zero divisors (S-wea...
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Suppose G is a p-mixed splitting abelian group and R is a commutative unitary ring of zero characteristic such that the prime number p satisfies p / ∈ inv(R)∪ zd(R). Then R(H) and R(G) are canonically isomorphic R-group algebras for any group H precisely when H and G are isomorphic groups. This statement strengthens results due to W.May published in J.Algebra (1976) and to W.Ullery published in...
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We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in idea...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.2307/2041099