We give a Decomposition Theorem for a family of Hopf algebras containing the well-know family of Taft Hopf algebras. Therefore, those indecomposable codes over this family of algebras (cf. [4]) is an indecomposable code over the studied case. We use properties of Hopf algebras to show that dual (in the module sense) of an ideal code is again an ideal code.

We study the core Hopf algebra underlying the renormalization Hopf algebra.

Let R be the valuation ring ofK, a finite extension of Qp containing a primitive pth root of unity, and let G be an elementary abelian p-group of order p, with dual group Ĝ. We construct a new family of triangular Hopf orders over R in KG, a proper subfamily whose duals are also triangular, and a proper subfamily of that family whose construction extends the truncated exponential construction o...