Koenig, Steffen (Prof. Dr.)Yirtici, Cigdem2021-01-192021-01-1920201744960356http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-112585http://elib.uni-stuttgart.de/handle/11682/11258http://dx.doi.org/10.18419/opus-11241Two large classes of algebras, Frobenius algebras and gendo-symmetric algebras, are characterised by thenexistence of a comultiplication with some special properties. Symmetric algebras are both Frobenius and gendo-symmetric. Kerner and Yamagata investigated two variations of gendo-symmetric algebras and in fact these two variations contain gendo-symmetric and Frobenius algebras. We call one of these variations gendo-Frobenius algebras. In this thesis, we construct a comultiplication for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius algebras and on gendo-symmetric algebras. Moreover, we show that Frobenius algebras are precisely those gendo-Frobenius algebras that have a counit compatible with this comultiplication.eninfo:eu-repo/semantics/openAccess510doctoralThesis