By Stefaan Caenepeel
Doi-Koppinen Hopf modules and entwined modules unify different types of modules which were intensively studied over the last a long time, similar to Hopf modules, graded modules, Yetter-Drinfeld modules. The publication provides a unified idea, with specialize in express thoughts generalizing the notions of separable and Frobenius algebras, and discussing family with break items, Galois thought and descent idea. each one bankruptcy of half II is dedicated to a selected nonlinear equation. The exposé is equipped in this type of approach that the analogies among the 4 are transparent: the quantum Yang-Baxter equation is expounded to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the lengthy equation to lengthy dimodules. The Frobenius-separability equation offers a brand new point of view to Frobenius and separable algebras.