NeutroVectorSpaces I

Recently, the concept of NeutroAlgebraic and AntiAlgebraic Structures were introduced and analyzed by
Florentin Smarandache. His new approach to the study of Neutrosophic Structures presents a more robust tool needed
for managing uncertainty, incompleteness, indeterminate and imprecise information. In this paper, we introduce for the
first time the concept of NeutroVectorSpaces. Specifically, we study a particular class of the NeutroVectorSpaces called
of type 4 S and their elementarily properties are presented. It is shown that the NeutroVectorSpaces of type 4 S may contain NeutroSubspaces of other types and that the intersections of NeutroSubspaces of type 4 S are not NeutroSubspaces.
Also, it is shown that if N V is a NeutroVector Space of a particular type and N W is a NeutroSubspace of N V, the
NeutroQuotientSpace N V /N W does not necessarily belong to the same type as N V.