关于有理模和余理想子代数的性质

In this paper, for some used conceptions and notations, we see ［1］ and ［2］.§1. Rational Module and Its Exact Sequence In ［1］, Cai Chuanreng and Cheng Huixiang have proved that relative Hopf modules and rational modules are one by one corresponding. In ［2］, Zhang Liangyun has given the dual relationship between relative Hopf modules. Naturally, we have a question to ask: is the dual module of a rational module still a rational module? This answer is affirmative. Let H be a Hopf …

The Properties of Rational Modules and Coideal Subalgebras

In this paper, we first prove that the dual module of a rational module is still, a rational module, and maximum rational modules keep their exact properties. Then, we give the Maschke theorem of the coideal subalgebra of quasi-Frobenius algebra, and give some equivalent conditions for the ideal subcoalgebra.