On Some Neutrosophic Algebraic Equations

This paper is devoted to studying linear equations, and quadratic equations over a neutrosophic field 𝐹(𝐼) and refined neutrosophic field 𝐹(𝐼1,𝐼2). This work introduces a full description of the solution's algorithm in 𝐹(𝐼) and 𝐹(𝐼1,𝐼2), and discusses the solution's algorithm for a linear system of neutrosophic equations over 𝐹(𝐼) and 𝐹(𝐼1,𝐼2) for the first time.

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

This paper is devoted to study for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers. This work introduces an algorithm to solve the linear Diophantine equation.

In this paper, we use the one dimensional AH-isometry to find the structure of the solutions of many neutrosophic differential equations. These equations will be handled by the algebraic direct image of the neutrosophic AH-isometry taken in one dimension.

International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications.

This work is dedicated to give the interested reader a good review and background in recent developments in the field of neutrosophic algebraic module theory.

In this paper, we give a review about neutrosophic linear spaces and their properties.

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.