Neutrosophic Vector Spaces

Abstract

The objective of this paper is to study neutrosophic vector spaces. Some basic definitions and properties of the classical vector spaces are generalized. It is shown that every neutrosophic vector space over a neutrosophic field (resp. a field) is a vector space. Also, it is shown that an element of a neutrosophic vector space over a neutrosophic field can be infinitely expressed as a linear combination of some elements of the neutrosophic vector space. Neutrosophic quotient spaces and neutrosophic vector space homomorphism are also studied.

Keywords

• Weak neutrosophic vector space
• strong neutrosophic vector space
• field
• neutrosophic field