楔积的值Gabriel算子与半素余代数
The valued Gabriel quiver of a wedge product and semiprime coalgebras
摘要：
通过对余代数的值Gabriel n的刻画，首次探讨了余代数的楔积的表示论.然后定义了半素余代数，并利用局部化技巧研究了它的余模范畴。特别地，我们证明了，无论其Gabriel余代数是局部有限的，任何单项半素fc-tame余代数是弦。我们还证明了Eisenbud-Griffith定理的一个较弱的版本，即任何遗传半质严格拟有限余代数是串行的。
英文摘要：
We make a first approach to the representation theory of the wedge product of coalgebras by means of the description of its valued Gabriel quiver. Then we define semiprime coalgebras and study its category of comodules by the use of localization techniques. In particular, we prove that, whether its Gabriel quiver is locally finite, any monomial semiprime fc-tame coalgebra is string. We also prove a weaker version of Eisenbud-Griffith theorem, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.
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