Equivalences between Categories of Modules and Categories of Comodules  

作　　者：Joost VERCRUYSSE 

机构地区：[1]Vrije Universiteit Brussel VUB, Pleinlaan 2, B-1050, Brussel, Belgium

出　　处：《Acta Mathematica Sinica,English Series》2008年第10期1655-1674,共20页数学学报（英文版）

摘　　要：We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 （2007）, 271 306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 （2006）, 2683-2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules.We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 （2007）, 271 306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 （2006）, 2683-2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules.

关 键 词：Galois comodules comatrix corings firm projectivity 

分 类 号：O153.3[理学—数学]