Zabarylo O. On representations of equipped partially ordered sets

The dissertation is devoted to investigate the representation theory problems for equipped partially ordered sets (posets) over the pair (R,C). For such posets the differentiation algorithms are constructed with the description on the categorical and matrix languages. With their help the criterion for an equipped poset to be one-parameter is proved. A full classification of the indecomposables is obtained, including description of the faithful equipped posets. It is also obtained a new, more simple proof of the representation-finiteness criterion, based on using of the differentiation tecknique.