ON THE TOPOLOGICAL STRUCTURES ON Γ-SEMIRINGS

  • Kostaq Hila Department of Mathematics & Computer Science, Faculty of Natural Sciences, University of Gjirokastra, Albania
  • Ilir Vardhami Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania.
  • Kristaq Gjino Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania.

Abstract

In this paper, we introduce some special classes of ideals in Γ-semirings called prime k-ideal, prime full k-ideal, prime ideals, maximal and strongly irreducible ideals. Considering and investigating properties of the collection A , T , M , B and S of all proper prime k-ideals, proper prime full k-ideals, maximal ideals, prime ideals and strongly irreducible ideals, respectively, of a Γ- semiring R, we construct the respective topologies on them by means of closure operator defined in terms of intersection and inclusion relation among these ideals of Γ-semiring R. The respective obtained topological spaces are called the structure spaces of the Γ-semiring R. We study a several principal topological axioms and properties in those structure spaces of Γ-semiring such as separation axioms, compactness and connectedness etc.

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Published
2013-07-12
How to Cite
Hila, K., Vardhami, I., & Gjino, K. (2013). ON THE TOPOLOGICAL STRUCTURES ON Γ-SEMIRINGS. European Scientific Journal, ESJ, 9(21). https://doi.org/10.19044/esj.2013.v9n21p%p