On prime spaces of neutrosophic extended triplet groups

Abstract

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.

Keywords

• weak commutative netg
• zariski topology
• topological representation
• equivalence of categories
• 20a15
• 18b30
• 54f65