### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 261-270 |

Number of pages | 10 |

Journal | Tamkang Journal of Mathematics |

Volume | 47 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2016 Sep |

### Keywords

- GCD
- Ideals lattice
- LCM
- Multiplicative lattice

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'A GCD and LCM-like inequality for multiplicative lattices'. Together they form a unique fingerprint.

## Cite this

Anderson, D. D., Aoki, T., Izumi, S., Ohno, Y., & Ozaki, M. (2016). A GCD and LCM-like inequality for multiplicative lattices.

*Tamkang Journal of Mathematics*,*47*(3), 261-270. https://doi.org/10.5556/j.tkjm.47.2016.1822