Flat cotorsion modules over Noether algebras
Flat cotorsion modules over Noether algebras
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DOI：
10.4171/dm/893
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发表时间：
2021-08
影响因子：
0.9
通讯作者：
Ryo Kanda;Tsutomu Nakamura
中科院分区：
文献类型：
--
作者：
Ryo Kanda;Tsutomu Nakamura
对于交换诺特环上的模有限代数，我们根据代数的素理想给出了平扭曲模的完整描述，作为交换诺特环的 Enochs 结果的推广。因此，我们证明点向 Matlis 对偶性给出了不可分解单射左模块的同类与不可分解平直扭曲右模块的同类之间的双射对应关系。这种对应关系是由齐格勒谱的基本对偶性导出的赫尔佐格同胚的明确实现。
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs’ result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable injective left modules and the isoclasses of indecomposable flat cotorsion right modules. This correspondence is an explicit realization of Herzog’s homeomorphism induced from elementary duality of Ziegler spectra.