The relation between the decomposition of comodules and coalgebras
| dc.creator | Zhang, Shouchuan | |
| dc.date | 2003-11-28 | |
| dc.date.accessioned | 2026-07-07T05:03:22Z | |
| dc.date.available | 2026-07-07T05:03:22Z | |
| dc.description | T. Shudo and H. Miyamito \cite{SM78} showed that $C$ can be decomposed into a direct sum of its indecomposable subcoalgebras of $C$. Y.H. Xu \cite {XF92} showed that the decomposition was unique. He also showed that $M$ can uniquely be decomposed into a direct sum of the weak-closed indecomposable subcomodules of $M$(we call the decomposition the weak-closed indecomposable decomposition) in \cite{XSF94}. In this paper, we give the relation between the two decomposition. We show that if $M$ is a full, $W$-relational hereditary $C$-comodule, then the following conclusions hold: (1) $M$ is indecomposable iff $C$ is indecomposable; (2) $M$ is relative-irreducible iff $C$ is irreducible; (3) $M$ can be decomposed into a direct sum of its weak-closed relative-irreducible subcomodules iff $C$ can be decomposed into a direct sum of its irreducible subcoalgebras. We also obtain the relation between coradical of $C$- comodule $M$ and radical of algebra $C(M)^*$ | |
| dc.description | 17pages | |
| dc.identifier | https://arxiv.org/abs/math/0311521 | |
| dc.identifier | http://arxiv.org/abs/math/0311521 | |
| dc.identifier | Science in China, 40 (1997), 25-29 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69388 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16w30 | |
| dc.title | The relation between the decomposition of comodules and coalgebras | |
| dc.type | text |