## Abstract

We provide a construction of monomial ideals in R = K[x, y] such that

µ(I

2

) < µ(I), where µ denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in

the ring R, we generalize the definition of a Freiman ideal which was introduced in J. Herzog,

G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case

of this characterization leads to some further investigations on µ(I

k

) that generalize some

results of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018), J. Herzog, M. Mohammadi

Saem, N. Zamani (2019), and J. Herzog, A. Asloob Qureshi, M. Mohammadi Saem (2019).

µ(I

2

) < µ(I), where µ denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in

the ring R, we generalize the definition of a Freiman ideal which was introduced in J. Herzog,

G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case

of this characterization leads to some further investigations on µ(I

k

) that generalize some

results of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018), J. Herzog, M. Mohammadi

Saem, N. Zamani (2019), and J. Herzog, A. Asloob Qureshi, M. Mohammadi Saem (2019).

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

Pages (from-to) | 847-864 |

Number of pages | 17 |

Journal | Czechoslovak Mathematical Journal |

Volume | 71 |

Issue number | 146 |

Publication status | Published - 2021 |