TY - JFULL AU - Lili Chen and Chao Yuan PY - 2016/4/ TI - Module and Comodule Structures on Path Space T2 - International Journal of Mathematical and Computational Sciences SP - 150 EP - 155 VL - 10 SN - 1307-6892 UR - https://publications.waset.org/pdf/10005391 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 111, 2016 N2 - On path space kQ, there is a trivial kQa-module structure determined by the multiplication of path algebra kQa and a trivial kQc-comodule structure determined by the comultiplication of path coalgebra kQc. In this paper, on path space kQ, a nontrivial kQa-module structure is defined, and it is proved that this nontrivial left kQa-module structure is isomorphic to the dual module structure of trivial right kQc-comodule. Dually, on path space kQ, a nontrivial kQc-comodule structure is defined, and it is proved that this nontrivial right kQc-comodule structure is isomorphic to the dual comodule structure of trivial left kQa-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule. ER -