论文标题
关于平坦尺寸模块的平坦和连贯性最多一个
On flatness and coherence with respect to modules of flat dimension at most one
论文作者
论文摘要
本文介绍和研究新模块的同源性能，即$ \ Mathcal f_1 $ -flat模块和$ \ Mathcal f_1^{\ fp} $ - 平面模块，其中$ \ Mathcal f_1 $ for f _1 $的$} f _ $} $ $ $ \ nmats f_1由有限呈现的元素组成的子类。这使我们引入了一个新的戒指，我们称我们为$ \ MATHCAL F_1^{\ fp} $ - 连贯的环，因为它们相对于$ \ Mathcal F_1^{\ fp} $ - 与平面模块相干的环一样，它们的表现很好。 $ \ Mathcal F_1^{\ fp} $ - 相干戒指的新类是一个大的戒指，它包括连贯的戒指，完美的戒指，半herseditary Rings和所有环$ r $，使得$ \ lim \ lim \ lim \ limits _ {\ lr}} \ lr} \ Mathcal p_1 = \ Mathcal p_1 = \ Mathcal f_1 $。作为满足$ \ lim \ limits _ {\ lr} \ MATHCAL P_1 = \ MATHCAL F_1 $图的特定情况。
This paper introduces and studies homological properties of new classes of modules, namely, the $\mathcal F_1$-flat modules and the $\mathcal F_1^{\fp}$-flat modules, where $\mathcal F_1$ stands for the class of right modules of flat dimension at most one and $\mathcal F_1^{\fp}$ its subclass consisting of finitely presented elements. This leads us to introduce a new class of rings that we term $\mathcal F_1^{\fp}$-coherent rings as they behave nicely with respect to $\mathcal F_1^{\fp}$-flat modules as do coherent rings with respect to flat modules. The new class of $\mathcal F_1^{\fp}$-coherent rings turns out to be a large one and it includes coherent rings, perfect rings, semi-hereditary rings and all rings $R$ such that $\lim\limits_{\lr}\mathcal P_1=\mathcal F_1$. As a particular case of rings satisfying $\lim\limits_{\lr}\mathcal P_1=\mathcal F_1$ figures the important class of integral domains.
