Injective Hull - Uniform Dimension and Injective Modules

Uniform Dimension and Injective Modules

An R module M has finite uniform dimension (=finite rank) n if and only if the injective hull of M is a finite direct sum of n indecomposable submodules.

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Famous quotes containing the words uniform and/or dimension:

    The maples
    Stood uniform in buckets, and the steam
    Of sap and snow rolled off the sugarhouse.
    Robert Frost (1874–1963)

    Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.
    Tom Wolfe (b. 1931)