Certain monomial ideals whose numbers of generators of powers descend
Certain monomial ideals whose numbers of generators of powers descend
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DOI：
10.1007/s00013-021-01596-y
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发表时间：
2020-05
影响因子：
0.6
通讯作者：
Reza Abdolmaleki;S. Kumashiro
中科院分区：
文献类型：
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作者：
Reza Abdolmaleki;S. Kumashiro
本文研究多项式环中单项理想的幂的极小生成元的个数。对于两个变量中的单项理想I，Eliahou，Herzog和Saem给出了最小生成元的数量的急剧下界。最近，Gasanova构造了单项式理想，使得对任意正整数，在此基础上，我们构造了一类单项式理想，使得对任意正整数，它提供了函数的一个最出乎意料的性质。单项理想也给出了一个特殊的例子，使得的Cohen-Macaulay型（或不可约指数）下降。
This paper studies the numbers of minimal generators of powers of monomial ideals in polynomial rings. For a monomial idealIin two variables, Eliahou, Herzog, and Saem gave a sharp lower boundfor the number of minimal generators ofwith. Recently, Gasanova constructed monomial ideals such thatfor any positive integern. In reference to them, we construct a certain class of monomial ideals such thatfor any positive integern, which provides one of the most unexpected behaviors of the function. The monomial ideals also give a peculiar example such that the Cohen–Macaulay type (or the index of irreducibility) ofdescends.