On prime spaces of neutrosophic extended triplet groups

This article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) NN, denoted by Prim(N){\rm{Prim}}\left(N). First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topologica...

Full description

Saved in:
Bibliographic Details
Main Authors: Zhou Xin, Xin Xiao Long
Format: Article
Language:English
Published: De Gruyter 2024-12-01
Series:Open Mathematics
Subjects:
Online Access:https://doi.org/10.1515/math-2024-0079
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) NN, denoted by Prim(N){\rm{Prim}}\left(N). First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topological space XX is an SSSS-space if and only if XX is homeomorphic to the space Prim(N){\rm{Prim}}\left(N) of some weak commutative NETG. In addition, we prove that there exists an adjunction between the dual category of weak commutative NETGs and the category of SSSS-spaces. Finally, we further study the categorical relation between idempotent weak commutative NETGs and that of SSSS-spaces, which leads to a conclusion that the category of idempotent weak commutative NETGs is equivalent to that of commutative idempotent semigroups.
ISSN:2391-5455