Abstract
For an Archimedean d-ring R and a positive derivation D on R, it is shown that \({D(R) \subseteq N(R)}\), where N(R) is the \({\ell}\)-radical of R.
Similar content being viewed by others
References
Bernau S.J., Huijsmans C.B.: Almost f-algebras and d-algebras. Math. Proc. Camb. Phil. Soc. 107, 287–308 (1990)
Birkhoff G., Pierce R.S.: Lattice-ordered rings. An. Acad. Brasil. Ci. 28, 41–69 (1956)
Boulabiar K.: Positive derivations on Archimedean almost f-rings. Order 19, 385–395 (2002)
Colville P., Davis G., Keimel K.: Positive derivations on f-rings. J. Aust. Math. Soc. 23, 371–375 (1977)
Diem J.E.: A radical for lattice-ordered rings. Pacific J. Math, 25, 71–82 (1968)
Henriksen, M., Smith, F.M.,: Some properties of positive derivations on f-rings. In: Ordered fields and real algebraic geometry (San Francisco, Calif., 1981), Contemp. Math., vol. 8, pp. 175–184. Amer. Math. Soc., Providence (1982)
Ma J., Redfield R.H.: Positive derivations on Archimedean lattice-ordered rings. Positivity 13, 165–191 (2009)
Toumi, M.: Continuous generalized (\({\theta, \phi}\))-separating derivations on archimedean almost f-algebras. Asian-European J. Math. 3, 1–17 (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by W. McGovern.
Rights and permissions
About this article
Cite this article
Ma, J., Zhang, Y. Positive derivations on Archimedean d-rings. Algebra Univers. 72, 163–166 (2014). https://doi.org/10.1007/s00012-014-0299-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-014-0299-7