Topological characterization of Gelfand and zero dimensional semirings

Jorge Vielma

Ecuador

Escuela Superior Politécnica del Litoral (ESPOL)

Facultad de Ciencias Naturales y Matemáticas

Luz Marchan

Ecuador

Escuela Superior Politécnica del Litoral (ESPOL)

Facultad de Ciencias Naturales y Matemáticas

Submitted: 2017-08-22

|

Accepted: 2018-02-09

|

Published: 2018-10-04

DOI: https://doi.org/10.4995/agt.2018.7952
Funding Data

Downloads

Keywords:

Zariski topology, D-topology, conmutative semiring, Gelfand semiring, zero dimensional semiring

Supporting agencies:

This research was not funded

Abstract:

Let R be a conmutative semiring with 0 and 1, and let Spec(R) be the set of all proper prime ideals of R. Spec(R) can be endowed with two topologies, the Zariski topology and the D-topology.  Let Max R denote the set of all maximals  prime ideals of R. We prove that the two topologies coincide on Spec(R) and on Max R if and only if R is zero dimensional and Gelfand semiring, respectively.
Show more Show less

References:

H. Al-Ezeh, Topological characterization of certain classes of lattices, Rend. Sem. Univ. Padova 83 (1990), 13-18.

M. L. Colasante, C. Uzcátegui and J. Vielma, Boolean algebras and low separation axioms, Topology Proceedings 34 (2009), 1-15.

N. Rafi and G. C. Rao, Topological characterization of certain classes of almost distributive lattice, J. Appl. Math. & Informatics 33, no. 3-4 (2015), 317-325. https://doi.org/10.14317/jami.2015.317

M. T. Sancho, Methods of conmutative algebra for topology, Universidad de Salamanca, Departamento de matemáticas, (1987).

C. Uzcátegui and J. Vielma, Alexandroff topologies viewed as closed sets in the Cantor cube, Divulg. Mat. 13, no. 1 (2005), 45-53.

Show more Show less