Skip to main content
SpringerLink
Log in

Tensor product of f-rings

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

In this paper we prove that the \(\ell \)-group tensor product of two Archimedean f-rings is again an f-ring. We will use this result to characterize multiplicative \(\ell \)-bimorphisms between unital f-rings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, M., Feil, T.: A First Course in Abstract Algebra: Rings, Groups, and Fields, 3rd edn. CRC Press, Boca Raton (2015)

    MATH  Google Scholar 

  2. Azouzi, Y., Ben Amor, M.A.: On von Neumann regular elements in \(f\)-rings. Algebra Univ. 78(1), 119–124 (2017)

    Article  MathSciNet  Google Scholar 

  3. Azouzi, Y., Ben Amor, M.A., Jaber, J.: The tensor product of \(f\)-algebras. Quaest. Math. 41(3), 359–369 (2018)

    Article  MathSciNet  Google Scholar 

  4. Ben Amor, M.A., Boulabiar, K.: Almost \(f\)-maps and almost \(f\)-rings. Algebra Univ. 69(1), 93–99 (2013)

    Article  MathSciNet  Google Scholar 

  5. Bigard, A., Keimel, K., Wolfenstein, S.: Groupes et Anneaux Réticulés. Lecture Notes in Mathematics, vol. 608. Springer, Berlin-New York (1977)

    Book  Google Scholar 

  6. Bleier, R.D.: Minimal vector lattice covers. Bull. Austral. Math. Soc. 5, 331–335 (1971)

    Article  MathSciNet  Google Scholar 

  7. Boulabiar, K., Toumi, M.A.: Lattice bimorphisms on \(f\)-algebras. Algebra Univ. 48(1), 103–116 (2002)

    Article  MathSciNet  Google Scholar 

  8. Buskes, G.J.H.M., Holland, J.: A note on the commutativity of archimedean almost-\(f\)-rings. New Zeland J. Math. 30, 25–29 (2001)

    MathSciNet  MATH  Google Scholar 

  9. Buskes, G.J.H.M., van Rooij, A.C.M.: The Archimedean \(l\)-group tensor product. Order 10(1), 93–102 (1993)

    Article  MathSciNet  Google Scholar 

  10. Buskes, G.J.H.M., Wickstead, A.W.: Tensor products of \(f\)-algebras. Mediterr. J. Math. 14(2):Art. 63, 10 (2017)

  11. Conrad, P.F.: Minimal vector lattice covers. Bull. Austral. Math. Soc. 4, 35–39 (1971)

    Article  MathSciNet  Google Scholar 

  12. Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94, 777–798 (1972)

    Article  MathSciNet  Google Scholar 

  13. Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87–106 (1974)

    Article  MathSciNet  Google Scholar 

  14. Grobler, J.J., Labuschagne, C.C.A.: The tensor product of Archimedean ordered vector spaces. In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 104, pp. 331–345. Cambridge University Press (1988)

  15. Grobler, J.J., Labuschagne, C.C.A.: An \(f\)-algebra approach to the Riesz tensor product of Archimedean Riesz spaces. Quaest. Math. 12(4), 425–438 (1989)

    Article  MathSciNet  Google Scholar 

  16. Henriksen, M., Isbell, J.R.: Lattice-ordered rings and function rings. Pac. J. Math. 12, 533–565 (1962)

    Article  MathSciNet  Google Scholar 

  17. Johnson, D.G.: The completion of an Archimedean \(f\)-ring. J. Lond. Math. Soc. 40, 493–496 (1965)

    Article  MathSciNet  Google Scholar 

  18. Martinez, J.: Tensor products of partially ordered groups. Pac. J. Math. 41, 771–789 (1972)

    Article  MathSciNet  Google Scholar 

  19. Steinberg, S.A.: Lattice-Ordered Rings and Modules. Springer, New York (2010)

    Book  Google Scholar 

Download references

Acknowledgements

Funding was provided by South African Agency for Science and Technology Advancement (Grant No. 120112).

Author information

Authors and Affiliations

  1. Research Laboratory of Algebra, Topology, Arithmetic, and Order, Department of Mathematics, Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis-El Manar University, 2092-El, Manar, Tunisia

    Mohamed Amine Ben Amor

Authors
  1. Mohamed Amine Ben Amor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Amine Ben Amor.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ben Amor, M.A. Tensor product of f-rings. Positivity 25, 663–668 (2021). https://doi.org/10.1007/s11117-020-00780-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11117-020-00780-8

Keywords

Mathematics Subject Classification

Search

Navigation