Radicals of Generalized Matrix Rings and Their Applications in Hopf Algebras and Directed Graphs
نویسندگان
چکیده
It is proved that radical of every generalized ring is a G-graded ideal when its index is an abelian group G. The relation between radicals of generalized rings and Γ-rings is given. The explicit formulas for generalized ring A and radical properties r = rb, rl, rj , rn are obtained: r(A) = g.m.r(A) = ∑ {r(Aij) | i, j ∈ I}. The relation between the radicals of path algebras and connectivity of directed graphs is given. That is, every weak component of directed path D is a strong component iff every unilateral component of D is a strong component iff the Jacobson radical of path algebra A(D) is zero iff the Baer radical of path algebra A(D) is zero. 2000 Mathematics subject Classification: 16w30, 05Cxx.
منابع مشابه
Generalized Matrix Algebras and Their Applications
The relations between the radicals of path algebras and connectivity of directed graphs are given. The relations between radicals of generalized matrix rings and Γrings are given. All the coquasitriangular structures of group algebra kG are found when G is a finitely generated abelian group. 2000 Mathematics subject Classification: 16w30, 05Cxx.
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