模的嵌入问题和QF—余代数

Embedding Some Modules in Projectives and QF-Coalgebras

本文首先在文[3]工作基础上进一步讨论了“每个有限生成模嵌入自由模”的环类,这类环称为FGF一环,接着引进了一类比FGF一环和Quasi-完全环更为广泛的环类,这类环称为FGFF环,即“每个有限生成平坦模嵌入自由模”的环类,我们讨论了这类环的各种特征性质及其与已知一些重要环类间的关系讨论这一问题的主要背景是文[2]-[9],[12][18].本文并讨论QF一余代数,得到了一系列很有意义的结果.

First we cliscuss the class of rings over.which every finitely generated module imbeds in aprojective. Such rings are called FGF-rings which are introduced by C. Faith in [3]. Second, we in-troduce a new class of rings which are called FGFF-rings,over which every fmitely generated flatmodule imbeds in a projective. We characterize such rings in many ways and give some relations be-tween FGFF-rings and other important rings. The back ground of this work is based on papers [2]-[9].[12]and [18]. Finally, we discuss QF-coalgebras and give a series of new results about it.