关于伪紧余代数、余挠对和弦余代数

Pseudocompact Coalgebras,Cotorsion Pairs and Some Characterizations of String Coalgebras

本文利用箭图和拓扑伪紧空间研究了K-余代数及其表示.定义了域K上的伪紧K-余代数,研究了伪紧K-余代数和K-代数范畴之间的关系,研究了余挠对和余模逼近,描述了余倾斜余挠对.通过有限维的支撑子余代数和基本的路余代数研究了弦余代数.

We develop a technique for the study of K-coalgebras and their representations by applying quivers and topologically pseudocompact spaces.A definition of pseudocompact K-coalgebra over a field K is introduced,and we study the relations of categories between pseudocompact K-coalgebras and K-algebras.Cotorsion pairs and approximations of comodules are investigated and the cotilting cotorsion pair is described.String coalgebras are studied by means of finite dimensional support subcoalgebras and the basic path K-coalgebras.