Some properties of positive derivations on f-rings II


  • R. H. Redfield Hamilton College





A counterexample is provided to show that Theorem 10(b)(i)  in the article “Some properties of positive derivations on f-rings” by Henriksen and Smith is false. Correct proofs are given for some results in the paper that use Theorem 10(b)(i) in their proofs.

Keywords: lattice-ordered ring, f-ring, positive derivation, polynomial ring.


A. Bigard, K. Keimel, S. Wolfenstein, Groupes et Anneaux Réticulés, Lecture Notes in Mathematics 608, Springer-Verlag, Berlin, 1977, ISBN 3-540-08436-3.

P. Colville, G. Davis, K. Keimel, Positive derivations on f-rings, J. Australian Math. Soc. 23 (1977), 371-375.

M. Darnel, Theory of Lattice-ordered Groups, Marcel Dekker, New York, 1995, ISBN 0-8247-9326-9.

M. Henriksen, F. A. Smith, Some properties of positive derivations on f-rings, Contemporary Math. 8 (1982), 175-184.

S. Steinberg, Lattice-ordered Rings and Modules, Springer, New York, 2010, ISBN 978-1-4419-1720-1.

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