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Algebra universalis

, 79:14 | Cite as

Representation of real Riesz maps on a strong f-ring by prime elements of a frame

  • Akbar Ali Estaji
  • Abolghasem Karimi Feizabadi
  • Batool Emamverdi
Article
  • 28 Downloads

Abstract

In classical topology, it is proved that for a topological space X, every bounded Riesz map \(\varphi :C (X) \rightarrow {\mathbb {R}}\) is of the from \({\hat{x}}\) for a point \(x\in X\). In this paper, our main purpose is to prove a version of this result by lattice-valued maps. A ring representation of the from \(A\rightarrow {\mathbb {R}}\) is constructed. This representation is denoted by \(\widetilde{p_c}\) that is an onto f-ring homomorphism for every \(p\in \Sigma L\), where its index c, denotes a cozero lattice-valued map. Also, it is shown that for every Riesz map \(\phi :A\rightarrow {\mathbb {R}} \) and \(c\in F(A, L)\) with specific properties, there exists \(p\in \Sigma L\) such that \(\phi =\phi (1)\widetilde{p_c}\).

Keywords

Frame Dedekind cut Strong f-ring Lattice-valued map 

Mathematics Subject Classification

06D22 54C30 13A15 

Notes

Acknowledgements

The authors would like to thank the referee for careful reading and valuable comments and suggestions relating to this work. Also, we thank Prof. M. M. Ebrahimi for a thorough scrutiny of the first version of this paper, and for comments which have improved the exposition.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Akbar Ali Estaji
    • 1
  • Abolghasem Karimi Feizabadi
    • 2
  • Batool Emamverdi
    • 1
  1. 1.Faculty of Mathematics and Computer SciencesHakim Sabzevari UniversitySabzevarIran
  2. 2.Department of Mathematics Gorgan BranchIslamic Azad UniversityGorganIran

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