Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T06:43:17.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizing f-rings

Published online by Cambridge University Press:  18 May 2009

Peter D. Colville
Peter D. Colville
Affiliation:
Ballarat Institute of Advanced Education, Mt. Helen, Victoria 3350, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Birkhoff and Pierce [2] introduced the class f-rings—those lattice-ordered rings R which satisfy the additional condition that if a, b, and c are positive elements of R and if a ∧ b = 0, then ac ∧ b = 0 = ca ∧ b. They showed that f-rings may be characterized as lattice-ordered rings which are subdirect products of totally-ordered rings.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 88 - 90
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Bernau, S. J., Unique representation of archimedean lattice groups and normal archimedean lattice rings, Proc. London Math. Soc. 15 (1965), 599–631.CrossRefGoogle Scholar
2.Birkhoff, G. and Pierce, R. S., Lattice-ordered rings, An. Acad. Brasil Sci. 28 (1956), 41–69.Google Scholar
3.Fuchs, L., Partially ordered algebraic systems. International Series of Monographs on Pure and Applied Mathematics (1963).Google Scholar
4.Goffman, C., A class of lattice-ordered algebras, Bull. Amer. Math. Soc. 64 (1958), 170–173.CrossRefGoogle Scholar
5.Hayes, A., A characterisation of f-rings without non-zero nilpotents, J. London Math. Soc. 39 (1964), 706–707.CrossRefGoogle Scholar
6.Johnson, D. G., A structure theory for a class of lattice-ordered rings, Acta Math. 104 (1960), 163–205.CrossRefGoogle Scholar