A Note on "Modules, Comodules, and Cotensor Products over Frobenius Algebras"

这是 Abram 的纸上的笔记“模块， Comodules，和 Cotensor Productsover Frobenius 代数学，代数学的杂志”(1999 ) 。用坐标最近由 Kadison 开发了的 Frobenius 的应用程序，一个人以 comultiplication 为 Frobeniusalgebras 有 Abram 的描述的一个直接证明(看见 L。Kadison (1999 )) 。为任何 Frobenius 代数学，由使用明确的 comultiplication，在模块的范畴和 comodules 的范畴之间的明确的通讯被获得。而且，与这，我们在对 cotensor 的角函子描述上给很简化的证明和 improveAbram 的结果函子。

This is a note on Abrams＇ paper ＂Modules, Comodules, and Cotensor Products over Frobenius Algebras, Journal of Algebras＂ （1999）. With the application of Frobenius coordinates developed recently by Kadison, one has a direct proof of Abrams＇ characterization for Frobenius algebras in terms of comultiplication （see L. Kadison （1999））. For any Frobenius algebra, by using the explicit comultiplication, the explicit correspondence between the category of modules and the category of comodules is obtained. Moreover, with this we give very simplified proofs and improve Abrams＇ results on the Hom functor description of cotensor functor.