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2 results

  • The singular ideal and radicals

  • Part of
  • Miguel Ferrero, Edmund R. Puczyłowski
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 64 / Issue 2 / April 1998
    Published online by Cambridge University Press:
    09 April 2009, pp. 195-209
    Print publication:
    April 1998
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  • Some properties of the singular ideal are established. In particular its behaviour when passing to one-sided ideals is studied. Obtained results are applied to study some radicals related to the singular ideal. In particular a radical S such that for every ring R, S(R) and R/S(R) are close to being a singular ring and a non-singular ring, respectively, is constructed.

  • FPF Rings and Some Conjectures of C. Faith

  • S. S. Page
  • Journal:
    Canadian Mathematical Bulletin / Volume 26 / Issue 3 / 01 September 1983
    Published online by Cambridge University Press:
    20 November 2018, pp. 257-259
    Print publication:
    01 September 1983
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  • A left FPF ring is a ring R such that every finitely generated faithful left R -module generates the category of left R-modules. It is shown that such rings split into R = A⊕B, where A is a two sided ideal, and A contains the left singular ideal of R as an essential submodule. If R is FPF on both sides B is two sided too, and R is the product of A and B. An example shows this is the best possible and that right FPF does not imply left FPF.