In this paper, we continue to study and investigate the homological objects related to s-pure and neat exact sequences of modules and module homomorphisms. A right module A is called max-flat if \({\text {Tor}}_{1}^{R}(A, R/I)= 0\) for any maximal left ideal I of R. A right module B is said to be max-cotorsion if \({\text {Ext}}^{1}_{R}(A,B)=0\) for any max-flat right module A. We characterize some classes of rings such as perfect rings, max-injective rings, SF rings and max-hereditary rings by max-flat and max-cotorsion modules. We prove that every right module has a max-flat cover and max-cotorsion envelope. We show that a left perfect right max-injective ring R is QF if and only if maximal right ideals of R are finitely generated. The max-flat dimensions of modules and rings are studied in terms of right derived functors of \(-\otimes -\). Finally, we study the modules that are injective and flat relative to s-pure exact sequences.

在本文中，我们将继续研究和研究与s-pure和模块的纯净精确序列以及模块同态有关的同源对象。如果\（{\ text {Tor}} _ {1} ^ {R}（A，R / I）= 0 \）对于R的任何最大左理想I，则右模块A称为最大展平。如果任何最大扁平右模块A的\（{\ text {Ext}} ^ {1} _ {R}（A，B）= 0 \），则右模块B被称为最大扭曲。。我们通过最大扁平和最大扭曲模块来表征某些类型的环，例如完美环，最大注入环，SF环和最大遗传环。我们证明每个正确的模块都有一个最大扁平盖和一个最大扭曲包络。我们证明，当且仅当R的最大右理想被有限生成时，左理想右最大内射环R才是QF 。根据\（-\ otimes-\）的右派生函子研究模块和环的最大扁平尺寸。最后，我们研究了相对于s-pure精确序列具有内射性和平坦性的模块。