Some topology on zero-dimensional subrings of product of rings | Zendy

Hassan Mouadi | Zendy; Driss Karim | Zendy

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Some topology on zero-dimensional subrings of product of rings

Author(s) -

Hassan Mouadi,

Driss Karim

Publication year - 2020

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2014589m

Subject(s) - mathematics , topology (electrical circuits) , zero (linguistics) , ultrafilter , direct limit , limit (mathematics) , product topology , ring (chemistry) , product (mathematics) , general topology , point (geometry) , pure mathematics , discrete mathematics , combinatorics , topological space , mathematical analysis , geometry , philosophy , linguistics , chemistry , organic chemistry

Let R be a ring and {Ri}i?I a family of zero-dimensional rings. We define the Zariski topology on Z(R,?Ri) and study their basic properties. Moreover, we define a topology on Z(R,?Ri) by using ultrafilters; it is called the ultrafilter topology and we demonstrate that this topology is finer than the Zariski topology. We show that the ultrafilter limit point of a collections of subrings of Z(R,?Ri) is a zero-dimensional ring. Its relationship with F-lim and the direct limit of a family of rings are studied.

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