Extensions are used in algebra to construct new objects out of a pair of simple structures, or also to decompose complicated objects into related simple parts. It is the aim of this thesis to give a survey of an extension theory for Hopf algebras. Extensions are characterized as ceratin types of exact sequences. Every extension gives rise to a "so-called" abelian matched of Hopf algebras, and isomorphic extensions belong to the same matched pair. The set of isomorphism classes of extensions belonging to the same abelian matched pair carries a Baer-type abelian group structure. It is shown to be isomorphic to the second cohomology group of the matched pair, thus making it possible to represent equivalence classes of extensions by bicross products of abelian matched pairs. The theory is illustrated by a couple of examples.

Extensions are used in algebra to construct new objects out of a pair of simple structures, or also to decompose complicated objects into related simple parts. It is the aim of this thesis to give a survey of an extension theory for Hopf algebras. Extensions are characterized as ceratin types of exact sequences. Every extension gives rise to a "so-called" abelian matched of Hopf algebras, and isomorphic extensions belong to the same matched pair. The set of isomorphism classes of extensions belonging to the same abelian matched pair carries a Baer-type abelian group structure. It is shown to be isomorphic to the second cohomology group of the matched pair, thus making it possible to represent equivalence classes of extensions by bicross products of abelian matched pairs. The theory is illustrated by a couple of examples.

Naloga se ukvarja s spektri realnih števil. Za te potrebe je raziskovalec definiral funkciji spodnji in zgornji del, nato pa še funkcijo ulomljenih del.