Some aspects of radical theory for fully ordered Abelian groups

Barry J. Gardner

Commentationes Mathematicae Universitatis Carolinae (1985)

  • Volume: 026, Issue: 4, page 821-837
  • ISSN: 0010-2628

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Gardner, Barry J.. "Some aspects of radical theory for fully ordered Abelian groups." Commentationes Mathematicae Universitatis Carolinae 026.4 (1985): 821-837. <http://eudml.org/doc/17429>.

@article{Gardner1985,
author = {Gardner, Barry J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {radical class; semisimple class; linearly ordered groups; hereditary class; hereditary lower radical class; skeletons},
language = {eng},
number = {4},
pages = {821-837},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some aspects of radical theory for fully ordered Abelian groups},
url = {http://eudml.org/doc/17429},
volume = {026},
year = {1985},
}

TY - JOUR
AU - Gardner, Barry J.
TI - Some aspects of radical theory for fully ordered Abelian groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1985
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 026
IS - 4
SP - 821
EP - 837
LA - eng
KW - radical class; semisimple class; linearly ordered groups; hereditary class; hereditary lower radical class; skeletons
UR - http://eudml.org/doc/17429
ER -

References

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  1. S. A. Amitsur, A general theory of radicals, II. Radicals in rings and bicategorles, Amer. J. Math. 76 (1954), 100-125. (1954) MR0059256
  2. C. G. Chehata R. Wiegandt, Radical theory for fully ordered groups, Mathematica (Cluj) 20 (1978), 143-157. (1978) MR0530451
  3. L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford, London, New York, Paris, 1963. (1963) Zbl0137.02001MR0171864
  4. B. J. Gardner, Some current issues in radical theory, Math. Chronicle 8 (1979), 1-23. (1979) Zbl0414.16003MR0564686
  5. B. J. Gardner, Small ideals in radical theory, Acta Math. Hungar. 43 (1984), 287-294. (1984) Zbl0536.16011MR0733860
  6. K. Hrbacek T. Jech, Introduction to Set Theory, Marcel Dekker, New York and Basel, 1978. (1978) MR0491188
  7. J. Jakubik, On the lattice of radical classes of linearly ordered groups, Studia Sci. Math. Hungar.16 (1981), 77-86. (1981) Zbl0465.06012MR0703644
  8. J. Jakubik, On the lattice of semisimple classes of linearly ordered groups, Časopis Pěst. Mat. 108 (1983), 183-190. (1983) Zbl0524.06027MR0704063
  9. J. Jakubik, On radical classes of abelian linearly ordered groups, submitted. Zbl0579.20034
  10. A. G. Kuroš, Radicals in the theory of groups, Colloq. Math. Soc. J. Bolyai 6 (1973), 271-296. [Russian original: Sibirsk. Mat. Zh. 3 (1962), 912-931.] (1973) MR0345997
  11. G. Pringerová, Covering condition in the lattice of radical classes of linearly ordered groups, Math. Slovaca 33 (1983), 363-369. (1983) MR0720506
  12. G. Pringerová, On semisimple classes of abelian linearly ordered groups, Časopis Pěst. Mat. 108 (1983), 40-52. (1983) MR0694139
  13. P. Ribenboim, Théorie des Valuations, Presses de l'Université de Montréal, Montréal, 1965. (1965) Zbl0139.26201MR0249425
  14. W. Sierpiński, Cardinal and Ordinal Numbers, PWN-Polish Scientific Publishers, Warsaw, 1965. (1965) MR0194339

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