International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

2690-6805ISSN (Online) 2692-6148ISSN (Print)

On Refined Neutrosophic R-module

Necati Olgun , Ahmed Hatip

Modules are one of the fundamental and rich algebraic structure concerning some binary operations in the study of algebra. In this paper, some basic structures of&nbsp;refined&nbsp;neutrosophic R-modules and&nbsp;refined&nbsp;neutrosophic submodules in algebra are generalized. Some properties of&nbsp;refined&nbsp;neutrosophic R-modules and&nbsp;refined&nbsp;neutrosophic submodules are presented. More precisely, classical modules and&nbsp;refined&nbsp;neutrosophic rings are utilized. Consequently,&nbsp;refinedneutrosophic R- modules that are completely different from the classical modular in the structural properties are introduced. Also, neutrosophic R-module homomorphism is explained and some definitions and theorems are presented.&nbsp;&nbsp;

Vol. 7 Issue. 2 PP. 87-96, (2020)

On Refined Neutrosophic Vector Spaces I

M.A. Ibrahim , A.A.A. Agboola , B.S. Badmus , S.A. Akinleye

The objective of this paper is to present the concept of a refined neutrosophic vector space. Weak(strong) refined neutrosophic vector spaces and subspaces, and, strong refined neutrosophic quotient vector spaces are studied. Several interesting results and examples are presented. It is shown that every weak (strong) refined neutrosophic vector space is a vector space and it is equally shown that every strong refined neutrosophic vector space is a weak refined neutrosophic vector space.

Vol. 7 Issue. 2 PP. 97-109, (2020)

Introduction to NeutroRings

Agboola A.A.A

The objective of this paper is to introduce the concept of NeutroRings by considering three NeutroAxioms (NeutroAbelianGroup (additive), NeutroSemigroup (multiplicative) and NeutroDistributivity (multiplication over addition)). Several interesting results and examples on NeutroRings, NeutroSubgrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms are presented. It is shown that the 1st isomorphism theorem of the classical rings holds in the class of NeutroRings.

Vol. 7 Issue. 2 PP. 62-73, (2020)

Classical Homomorphisms Between n-Refined Neutrosophic Rings

This paper studies classical homomorphisms between n-refined neutrosophic ring and m-refined neutrosophic ring. It proves that every m-refined neutrosophic ring&nbsp;&nbsp;is a homomorphic image of n-refined neutrosophic ring&nbsp;, where&nbsp;. Also, it presents a discussion of kernels and some corresponding isomorphisms between those rings.