A Remark on Left Pseudo-Artinian Rings

  • Gabriella D’Este
  • Claudia Menini
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)


Problem 2 of [2] asks whether or not any left pseudo-artinian ring is also a strongly left pseudo-artinian ring. Let us recall that a ring R is called left pseudo-artinian (resp. strongly left pseudo-artinian) if any finitely generated submodule of the minimal cogenerator E of the category R M of all left R-modules is artinian (resp. of finite length).


Path Algebra Artinian Ring Injective Hull Injective Envelope Semilocal Ring 


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  1. [1]
    D. DIKRANIAN — A. ORSATTI On the structure of linearly compact rings, Abelian Groups and Modules, Udine 1984 , Springer Verlag Wien .Google Scholar
  2. [2]
    C. MENINI — A. ORSATTI Topologically left artinian rings, to appear on the Journal of Algebra.Google Scholar
  3. [3]
    B. OSOFSKY An example of a cyclic artinian module of infinite length, unpublished (communicated by D. EISENBUD to the second author).Google Scholar
  4. [4]
    C.M. RINGEL Tame Algebras, Springer LMN 831 (1980) , 137–287.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • Gabriella D’Este
    • 1
  • Claudia Menini
    • 2
  1. 1.Università di PadovaItaly
  2. 2.Università di FerraraItaly

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