Morita Theory for Comodules Over Corings
Morita Theory for Comodules Over Corings
复制标题
森田共模相对于核心的理论
DOI：
10.1080/00927870902747993
复制
发表时间：
2007
影响因子：
0.7
通讯作者：
J. Vercruysse
中科院分区：
文献类型：
--
作者：
G. Böhm;J. Vercruysse
根据Kato和Ohtake的一个定理，任何（不一定是严格的）Morita context在Morita context中导出两个环的模范畴的适当子范畴之间的等价。这些实际上是非幺元子环的紧致模的范畴。我们将这一结果应用到各种森田上下文相关联的一个comomoacquisition的A-核心？这允许扩展（弱和强）结构定理在文献中，特别是超出的情况下，当任何的核心？或者余模是仿射生成的，并且是投射的A-模。也就是说，我们得到了？余模和实模范畴的一个坚实的环R，这是一个理想的自同态代数结束？（二）。对于余可分核的强投射余模，我们证明了一个强结构定理，该定理只假设标准映射是满射的。
By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings in the Morita context. These are in fact categories of firm modules for non-unital subrings. We apply this result to various Morita contexts associated to a comodule Σ of an A-coring ?. This allows to extend (weak and strong) structure theorems in the literature, in particular beyond the cases when any of the coring ? or the comodule Σ is finitely generated and projective as an A-module. That is, we obtain relations between the category of ?-comodules and the category of firm modules for a firm ring R, which is an ideal of the endomorphism algebra End ?(Σ). For a firmly projective comodule of a coseparable coring we prove a strong structure theorem assuming only surjectivity of the canonical map.