NeutroVectorSpaces I

Abstract

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 4S and their elementarily properties are presented. It is shown that the NeutroVectorSpaces of type 4S may contain NeutroSubspaces of other types and that the intersections of NeutroSubspaces of type 4S are not NeutroSubspaces.
Also, it is shown that if NV is a NeutroVector Space of a particular type and NW is a NeutroSubspace of NV , the
NeutroQuotientSpace NV /NW does not necessarily belong to the same type as NV .