On Submoduloids of a Moduloid on Nexus

In this paper, the submoduloid of a moduloid on nexus that is generated by a subset, cyclic submoduloid and bounded sets are defined and the properties of structures on it are investigated. Also, the fractions of a moduloid on nexus are defined and shown to be isomorphic with a moduloid on nexus

Soft nexuses

AbstractIn this paper, we define soft nexuses over a nexus N. After that we define the notions cyclic soft nexus, prime and maximal soft subnexuses and we obtain some results about the above definitions. Finally, we define the integer number induced by soft nexus (α,A) and denoted by |(α,A)| and show that for any n∈ℵ, there exists soft nexus (α,A), such that |(α,A)|=n