ON THE TRANSFINITE POWERS OF THE JACOBSON RADICAL OF A DICC RING

  • Albu, Toma ;
  • Teply, Mark L.
  • Published : 2001.11.01

Abstract

A ring is a DICC ring if every chain of right ideals in-dexed by the integers stabilizes to the left or to the right or to both sides. A counterexample is given to an assertion of karamzadeh and Motamedi that a transfinite power of the Jacobson radical of a right DICC ring is zero. we determine the behavior of the transfinite powers of the Jacobson radical relative to a torsion theory and consequently can obtain their correct behavior in the classical setting.

Keywords

Jacobson radical;torsion theory;DICC module

References

  1. Abelian Group Theory Double Infinite Chain Conditions B. L. Ososfky;R. Gobel(ed.);E.A. Walker
  2. Pitman Monographs v.29 Torsion Theories J. S. Golan
  3. J. Algebra v.85 The Kernels of Completions Maps and a Relative Form of Nakayama's Lemma T. Porter
  4. J. Algebra v.229 The Nilpotence of the t-closed Prime Radical in Rings t-Krull Dimension T. Albu;G. Krause;M. L. Teply
  5. Comm. Algebra v.22 On α-DICC modules O. A. S. Karamzadeh;M. Motamedi
  6. J. Algebra v.107 On modules with DICC M. Contessa
  7. Contemp. Math., AMS v.259 The Double Infinite Chain Condition and Generalized Deviations of Posets and Modules, in Proc. Internat. Conf. on Algebra and its Applications, Athens, Ohio, March, 1999 T. Albu;M. L. Teply
  8. Relative Finiteness in Module Theory T. Albu;C. Nastasescu
  9. J. Algebra v.105 On DICC rings M. Contessa
  10. J. Algebra v.101 On rings and modules with DICC M. Contessa
  11. Math. Research v.103 Topics in Torsion Theory P. E. Bland