Notes on subsemigroups of Nm0(+)

Abstract

The paper summarizes and extends the knowledge of various subsemigroups of N m 0 (+) (= N0(+)m). It creates a theoretical basis for further study in this area and applications in other areas, such as the investigation of context-free languages. The last chapter introduces the notion of pure subsemigroups and presents one construction of a pure subsemigroup to a chosen semisubgroup of N m 0 (+).