A GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES

淡江大學機構典藏 > 淡江出版期刊 > 淡江數學期刊 > 第47卷第3期 > Item 987654321/109350

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題名:	A GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES
作者:	Aoki, Takashi Izumi, Shuzo Ohno, Yasuo Ozaki, Manabu
關鍵詞:	multiplicative lattice
日期:	2016-09
上傳時間:	2017-01-17 09:31:13 (UTC+8)
出版者:	淡江大學出版中心
摘要:	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.
關聯:	Tamkang Journal of Mathematics 47(3), pp.261-270
DOI:	10.5556/j.tkjm.47.2016.1822
顯示於類別:	[淡江數學期刊] 第47卷第3期

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