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nLab > Latest Changes: irreducible element

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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeAug 26th 2018

    Add missing nullary condition; note unbiased version.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorBartek
    • CommentTimeSep 15th 2019
    So the unbiased definition says "x is irreducible if, whenever it is written as a product of a finite list of elements, at least one element in the list is invertible."

    Maybe I'm being dumb, but say that we write x as a unary product of the finite list (x), doesn't that definition imply that x must be invertible?
    • CommentRowNumber3.
    • CommentAuthorOscar_Cunningham
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    You’re right. How about “whenever it’s an associate of a product it’s an associate of an element”?

    • CommentRowNumber4.
    • CommentAuthorRodMcGuire
    • CommentTimeSep 15th 2019

    If this gets fixed can it also be expanded to explicitly apply to the meet or join irreducible elements of a partial order / semi-lattice / lattice?

1 to 4 of 4

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