An algebraic perspective on neutrosophic sets: fields and linear spaces

Subject Areas : General algebraic systems

V. Cetkin ¹ (Department of Mathematics, Kocaeli University, 41001, Kocaeli, Turkey)
B. Pazar Varol ² (Department of Mathematics, Kocaeli University, 41001, Kocaeli, Turkey)
H. Aygun ³ (Department of Mathematics, Kocaeli University, 41001, Kocaeli, Turkey)

Received: 2020-05-31 Accepted : 2021-07-27 Published : 2021-09-01

Keywords: Field, Neutrosophic set, single valued neutrosophic set, homomorphism, linear space,

Abstract :

In this work, we intend to introduce and study another algebraic structure of single-valued neutrosophic sets called neutrosophic field as a continuation of our investigations on neutrosophic algebraic structures. For this goal, we define the concept of neutrosophic fields and observe some of their basic characteristics and properties. Then we give the definition of a neutrosophic linear space over the proposed neutrosophic field and consider its fundamental properties.

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