Graduate Program in Mathematics.Kanuni, Müge.Sütlü, Serkan.2023-03-162023-03-162007.MATH 2007 S88https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15233The main objective of this thesis is to study incidence coalgebras and incidence Hopf algebras. To this end, we first introduced algebras and coalgebras in a unified manner and investigated the the duality between them. Then by introducing the concepts of incidence algebra and reduced incidence algebra, we studied incidence coalgebra and incidence Hopf algebra in detail. By concluding, we gave a brief discussion of Galois connection for incidence Hopf algebras.30cm.Algebra.Hopf algebras.viii, 182 leaves;