Correction to: On the topological mass lattice groups

The Original Article was published on 24 January 2019

Correction to: Positivity (2019) 23:811–827 https://doi.org/10.1007/s11117-018-0639-5

  1. (i)

    In the first assertion of the Lemma 1 in [2], it is necessary that \(e\le y\). Note. By adding the above condition in the first assertion of the Lemma 1, this assertion holds in every unperforated partially ordered abelian group. In fact the condition lattice is redundant (see [1], p. 19 and Proposition 1.24).

  2. (ii)

    In the middle of page 819 of [2] (after the definition 9), the assertion “It is clear that G is Archimedean, if and only if, every element of G is regular” is not true without condition mass on G. In fact the corrected statement is as follows.

    • One can see that if G is Archimedean, then every element of G is regular and the converse is not true in general. But, if G is a mass group, then the converse is true.

References

  1. 1.

    Goodearl, K.R.: Partially Ordered Abelian Groups with Interpolation, A.M.S. Mathematical Surveys and Monographs, No. 20, American Mathematical Society, Providence, RI, 1986. MR 0845783 (88f:06013)

  2. 2.

    Pourgholamhossein, M., Ranjbar, M.A.: On the topological mass lattice groups. Positivity 23(4), 811–827 (2019)

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Pourgholamhossein, M., Ranjbar, M.A. Correction to: On the topological mass lattice groups. Positivity 25, 289–290 (2021). https://doi.org/10.1007/s11117-020-00756-8

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Keywords

  • Lattice group
  • Mass group