right chain ring that is not a chain ring

Discussion in 'Math Research' started by Pavel, Feb 11, 2004.

  1. Pavel

    Pavel Guest


    Does anybody know where can be found some example of a right chain
    ring that is not a chain ring? I'd really appreciate such a ring
    without a Krull dimension. Thanks for answers if any.
    Pavel, Feb 11, 2004
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  2. Pavel

    Axel Vogt Guest

    Examples are often treated in exercises and i found one
    in Anderson & Fuller, Rings and Categories of Modules,
    Ex. 13 in §10: R = ring of upper triangular matrices of
    the form
    (a b)
    (0 q)

    a, b reals and q rational is asserted to be both artinian
    and noetherian on the left but none of that on the right.
    Besides left/right (for which i would try to interchange
    a and q) is it what you are looking for (no, i do not
    have it worked out)?

    N.B. i remember the non-commutating colleagues often did
    first look at endomorphisms/matrices while the notorious
    non-noetherians went for countable polynomials/sequences.
    Axel Vogt, Feb 11, 2004
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