Boundedness versus periodicity over commutative local rings
Boundedness versus periodicity over commutative local rings
复制标题
交换局部环上的有界性与周期性
DOI：
10.1090/s0002-9947-1990-0967311-0
复制
发表时间：
1990
影响因子：
1.3
通讯作者：
I. Peeva
中科院分区：
文献类型：
--
作者：
Vesselin Gasharov;I. Peeva
在交换分次局部Artin环上，构造了任意最小周期的周期模和具有有界Betti数的模的例子，这些模最终不是周期的。它们为D的一个猜想提供了反例。Eisenbud证明了交换局部环上具有有界Betti数的模最终是周期为2的周期模。然而，它被证明，该猜想持有环的小长度。
Over commutative graded local artinian rings, examples are constructed of periodic modules of arbitrary minimal period and modules with bounded Betti numbers, which are not eventually periodic. They provide counterexamples to a conjecture of D. Eisenbud, that every module with bounded Betti numbers over a commutative local ring is eventually periodic of period 2. It is proved however, that the conjecture holds over rings of small length.