Skip to main content
Log in

Ideal chains in radical theory

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

It is shown that in a well known characterization of radical classes, closure under unions of chains of ideals can be replaced by closure under unions of continuous well-ordered chains of ideals. Some consequences are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. G. Chehata and R. Wiegandt, Radical theory for fully ordered groups, Mathematica (Cluj), 20(43) (1978), 143–157.

    MathSciNet  Google Scholar 

  2. L. Fuchs and R. Göbel, Unions of slender groups, Arch. Math., 87 (2006), 6–14.

    Article  MATH  Google Scholar 

  3. B. J. Gardner, Strong semi-simplicity, Periodica Math. Hungar., 24 (1992), 23–35.

    Article  MATH  Google Scholar 

  4. B. J. Gardner and R. Wiegandt, Radical Theory of Rings, Marcel Dekker (2004).

  5. H. Kneser, Eine direkt Ableitung des Zornschen Lemmas aus dem Auswahlsaxiom, Math. Z., 53 (1950), 110–113.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. G. Leavitt and L. C. A. van Leeuwen, Rings isomorphic with all proper factorrings, in: Ring Theory, Proc. Antwerp Conf., Univ. Antwerp, 1978, Marcel Dekker (1979), pp. 783–798.

  7. H. Rubin and J. Rubin, Equivalents of the Axiom of Choice, North-Holland (1970).

  8. T. Szele, On Zorn’s lemma, Publ. Math. Debrecen, 1 (1950), 254–256.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. J. Gardner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gardner, B.J. Ideal chains in radical theory. Acta Math Hung 119, 181–187 (2008). https://doi.org/10.1007/s10474-007-7015-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-007-7015-4

Key words and phrases

2000 Mathematics Subject Classification

Navigation