IMI/Publicaţii/QRS/Ediţii/QRS v.21, n.1 (29), 2013/

Zariski-topology for co-ideals of commutative semirings

Authors: S. Ebrahimi Atani, S. Dolati Pishhesari and M. Khoramdel


Let R be a semiring and co-spec(R) be the collection of all prime strong co-ideals of R. In this paper, we introduce and study a generalization of the Zariski topology of ideals in rings to co-ideals of semirings. We investigate the interplay between the algebraic-theoretic properties and the topological properties of co-spec(R). Semirings whose Zariski topology is respectively T1, Hausdorff or cofinite are studied, and several characterizations of such semirings are given.


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