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2 results

  • Covers and Envelopes via Endoproperties of Modules

  • Lidia Angeleri-Hügel
  • Journal:
    Proceedings of the London Mathematical Society / Volume 86 / Issue 3 / May 2003
    Published online by Cambridge University Press:
    09 June 2003, pp. 649-665
    Print publication:
    May 2003

  • Let $R$ be a ring and $M_R$ be an $R$-module. We characterize the existence of ${\rm Add} M$-covers and ${\rm Add} M$-envelopes in terms of finiteness conditions of $M$ over its endomorphism ring. We then present some applications related to the existence of well-behaved direct sum decompositions for direct products of copies of $M$. Our results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings.

  • On Self-Injective Perfect Rings

  • Dolors Herbera, Ahmad Shamsuddin
  • Journal:
    Canadian Mathematical Bulletin / Volume 39 / Issue 1 / 01 March 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 55-58
    Print publication:
    01 March 1996
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  • Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.