Simplicity of iterated Ore extensions

Here we study the simplicity of an iterated Ore extension of a unital ring [Formula: see text]. We give necessary conditions for the simplicity of an iterated Ore extension when [Formula: see text] is a commutative domain. A class of iterated Ore extensions, namely the differential polynomial ring [Formula: see text] in [Formula: see text]-variables is considered. The conditions for a commutative domain [Formula: see text] of characteristic zero to be a maximal commutative subring of its differential polynomial ring [Formula: see text] are given, and the necessary and sufficient conditions for [Formula: see text] to be simple are also found.

Ore Extensions for the Sweedler’s Hopf Algebra H4

The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H4[z;σ] of automorphism type for the Sweedler′s 4-dimensional Hopf algebra H4. Firstly, we calculate all equivalent classes of twisted homomorphisms (σ,J) for H4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H4[z;σ] up to isomorphism.