Quasi-Hereditary Orders.
We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category . Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.
Let be a group, and be a semi-Hopf -algebra. We first show that the category of left -modules over is a monoidal category with a suitably defined tensor product and each element in induces a strict monoidal functor from to itself. Then we introduce the concept of quasitriangular semi-Hopf -algebra, and show that a semi-Hopf -algebra is quasitriangular if and only if the category is a braided monoidal category and is a strict braided monoidal functor for any . Finally,...
Almost quasitrivial and critical semimodules are studied.
Critical semimodules over congruence-simple semirings are studied.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.