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A GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES
並列摘要
Let A_1, . . . , A_n (n ≥ 2) be elements of an commutative multiplicative lattice. Let G(k) (resp., L(k)) denote the product of all the joins (resp., meets) of k 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). 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) and show that any inequality relationships are possible.
並列關鍵字
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延伸閱讀
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