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The injective spectrum of a right noetherian ring
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.jalgebra.2020.07.016 Harry Gulliver
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.jalgebra.2020.07.016 Harry Gulliver
This is the second of two papers on the injective spectrum of a right noetherian ring. In the prequel, we considered the injective spectrum as a topological space associated to a ring (or, more generally, a Grothendieck category), which generalises the Zariski spectrum. We established some results about the topology and its links with Krull dimension, and computed a number of examples. In the present paper, which can largely be read independently of the first, we extend these results by defining a sheaf of rings on the injective spectrum and considering sheaves of modules over this structure sheaf and their relation to modules over the original ring. We then explore links with the spectrum of prime torsion theories developed by Golan and use this torsion-theoretic viewpoint to prove further results about the topology.
中文翻译:
右诺特环的单射谱
这是关于右诺特环的单射谱的两篇论文中的第二篇。在前传中,我们将单射谱视为与环(或更一般地说,格罗腾迪克范畴)相关的拓扑空间,它概括了 Zariski 谱。我们建立了一些关于拓扑及其与 Krull 维的联系的结果,并计算了一些例子。在本文中,可以在很大程度上独立于第一个阅读,我们通过在单射谱上定义一组环来扩展这些结果,并考虑该结构层上的模块组及其与原始环上模块的关系。然后,我们探索与 Golan 开发的素扭转理论谱的联系,并使用这种扭转理论观点来证明有关拓扑的进一步结果。
更新日期:2020-12-01
中文翻译:
右诺特环的单射谱
这是关于右诺特环的单射谱的两篇论文中的第二篇。在前传中,我们将单射谱视为与环(或更一般地说,格罗腾迪克范畴)相关的拓扑空间,它概括了 Zariski 谱。我们建立了一些关于拓扑及其与 Krull 维的联系的结果,并计算了一些例子。在本文中,可以在很大程度上独立于第一个阅读,我们通过在单射谱上定义一组环来扩展这些结果,并考虑该结构层上的模块组及其与原始环上模块的关系。然后,我们探索与 Golan 开发的素扭转理论谱的联系,并使用这种扭转理论观点来证明有关拓扑的进一步结果。