In this paper, we introduce a new concept of generalized matrix rings and build up the general theory of radicals for g.m.rings. Meantime, we obtain rÌ„b(A) = g.m.rb(A) = âˆ‘ {rb(Aij) | i, j âˆˆ I} = rb(A)

Let H be a finite Hopf algebra with C H,H = C Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

The relations between the radicals of path algebras and connectivity of directed graphs are given. The relations between radicals of generalized matrix rings and Î“rings are given. All theâ€¦ (More)

Most of pointed Hopf algebras of dimension p with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations,â€¦ (More)

We obtain the formula computing the number of isomorphic classes of ramification systems with characters over group Sn (n 6= 6) and their representatives. 2000 Mathematics Subject Classification:â€¦ (More)

F. Abe, M. G. Albrow, S. R. Amendolia, D. Amidei, J. Antos, C. AnwayWiese, G. Apollinari, H. Areti, M. Atac, P. Auchincloss, F. Azfar, P. Azzi, N. Bacchetta, W. Badgett, M. W. Bailey, J. Bao, P. deâ€¦ (More)

Braided m-Lie algebras induced by multiplication and generalized matrix braided m-Lie algebras are introduced. The necessary and sufficient conditions for a braided m-Lie algebra to be a strictâ€¦ (More)

It is shown that an algebra Î› can be lifted with nilpotent Jacobson radical r = r(Î›) and has a generalized matrix unit {eii}I with each Ä“ii in the center of Î›Ì„ = Î›/r iff Î› is isomorphic to aâ€¦ (More)

We show that any pointed Hopf algebra with infinitesi-mal braiding associated to the conjugacy class of Ï€ âˆˆ Sn is infinite-dimensional, if either the order of Ï€ is odd, or Ï€ is a product of disjointâ€¦ (More)

Throughout this paper, k is a field, R is an algebra over k, and H is a Hopf algebra over k. We say that R# Ïƒ H is the crossed product of R and H if R# Ïƒ H becomes an algebra over k byâ€¦ (More)