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Freeness Of Hopf Algebras, Christopher David Walker
Freeness Of Hopf Algebras, Christopher David Walker
Theses Digitization Project
The Nichols-Zoeller freeness theorem states that a finite dimensional Hopf algebra is free as a module over any subHopfalgebra. We will prove this theorem, as well as the first significant generalization of this theorem, which was proven three years later. This generalization says that if the Hopf algebra is infinite dimensional, then the Hopf algebra is still free if the subHopfalgebra is finite dimensional and semisimple . We will also look at several other significant generalizations that have since been proven.
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Theses Digitization Project
A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.