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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109350


    Title: A GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES
    Authors: Aoki, Takashi
    Izumi, Shuzo
    Ohno, Yasuo
    Ozaki, Manabu
    Keywords: multiplicative lattice
    Date: 2016-09
    Issue Date: 2017-01-17 09:31:13 (UTC+8)
    Publisher: 淡江大學出版中心
    Abstract: Let A1,…,AnA1,…,An (n≥2)(n≥2) be elements of an commutative multiplicative lattice. Let G(k)G(k) (resp., L(k)L(k)) denote the product of all the joins (resp., meets) of kk of the elements. Then we show that
    L(n)G(2)G(4)⋯G(2⌊n/2⌋)≤G(1)G(3)⋯G(2⌈n/2⌉−1).
    L(n)G(2)G(4)⋯G(2⌊n/2⌋)≤G(1)G(3)⋯G(2⌈n/2⌉−1).
    In particular this holds for the lattice of ideals of a commutative ring. We also consider the relationship between
    G(n)L(2)L(4)⋯L(2⌊n/2⌋) and L(1)L(3)⋯L(2⌈n/2⌉−1)
    G(n)L(2)L(4)⋯L(2⌊n/2⌋) and L(1)L(3)⋯L(2⌈n/2⌉−1)

    and show that any inequality relationships are possible.
    Relation: Tamkang Journal of Mathematics 47(3), pp.261-270
    DOI: 10.5556/j.tkjm.47.2016.1822
    Appears in Collections:[Tamkang Journal of Mathematics] v.47 n.3

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