Tertychna O. Matrix representations of semigroups generated by idempotents with partial null multiplication.

The dissertation is devoted to the study of matrix representations of semigroups generated by idempotents. The main results of the dissertation are full classifications of semigroups generated by idempotents with partial null multiplication (abbreviated: IPN-semigroups) that have finite representation type (over any fixed field) and full classifications of finite IPN-semigroups of tame type; here one proves that any infinite IPN-semigroup has infinite representation type. With each IPN-semigroup one associates a quiver, in term of which one formulates all criterions of the dissertation. For any IPN-semigroup one indicates a connection between its representations and representations of the corresponding quiver. The matrix representations of the semigroup generated by three idempotents with cyclic null multiplication are classified.