Noetherianity of some degree two twisted commutative algebras
Noetherianity of some degree two twisted commutative algebras
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DOI：
10.1007/s00029-015-0205-y
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发表时间：
2016-04-01
影响因子：
1.4
通讯作者：
Snowden, Andrew
中科院分区：
文献类型：
--
作者：
Nagpal, Rohit;Sam, Steven V.;Snowden, Andrew
行列式理想的分解具有显著的稳定性：对于固定秩但维数增长的理想，分解项稳定（在适当的意义下）。人们可能想知道矩阵的坐标环上的其他理想或模序列是否也表现出类似的行为。我们表明，这确实是这样的。事实上，我们的主要定理在本质上更基本：它指出某些大代数结构（扭曲交换代数的例子）是诺特的。这些都是大型诺特代数结构的重要新例子，而且在某些方面与以前的例子有很大的不同。
The resolutions of determinantal ideals exhibit a remarkable stability property: for fixed rank but growing dimension, the terms of the resolution stabilize (in an appropriate sense). One may wonder if other sequences of ideals or modules over coordinate rings of matrices exhibit similar behavior. We show that this is indeed the case. In fact, our main theorem is more fundamental in nature: It states that certain large algebraic structures (which are examples of twisted commutative algebras) are noetherian. These are important newexamples of large noetherian algebraic structures, and ones that are in some ways quite different from previous examples.