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The Nil Radicals in Several Classes of Lattice-Ordered Rings

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Abstract

We characterize the nil radicals in some l-rings. Several sufficient conditions for the nil radicals of l-rings to be equal and nilpotent are given. The results improve corresponding ones of Birkhoff and Pierce. We also show that the ideal generated by a nil one-sided ideal which is contained in a nil one-sided l-ideal is nil.

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References

  1. G. Birkhoff and R. S. Pierce, Lattice-ordered rings, An. Acad. Brasil Ci., 28 (1956). 41–69.

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  2. Gao Ting, On the structure of a radical of lattice-ordered rings, J. of Math. Research and Exp., 17 (1997), 529–537.

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  3. D. G. Johnson, A structure theory for a class of lattice-ordered rings, Acta Math., 104 (1960), 163–215.

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Authors and Affiliations

  1. Department of Mathematics, Hebei Teachers' University (East Campus), Shijiazhuang, 050016, China E-mail

    Gao Ting

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  1. Gao Ting
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Ting, G. The Nil Radicals in Several Classes of Lattice-Ordered Rings. Acta Mathematica Hungarica 89, 205–210 (2000). https://doi.org/10.1023/A:1010655708091

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  • DOI: https://doi.org/10.1023/A:1010655708091

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