A GCD and LCM-like inequality for multiplicative lattices

Daniel D. Anderson, Takashi Aoki, Shuzo Izumi, Yasuo Ohno, Manabu Ozaki

研究成果: Article査読

抄録

Let A1, . . . , An (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.

本文言語English
ページ(範囲)261-270
ページ数10
ジャーナルTamkang Journal of Mathematics
47
3
DOI
出版ステータスPublished - 2016 9

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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