@article{Assaad_2024, title={A note on weak w-projective modules}, volume={55}, url={https://nzjmath.org/index.php/NZJMATH/article/view/336}, DOI={10.53733/336}, abstractNote={<p>Let $R$ be a ring. An $R$-module $M$ is a weak $w$-projective module if ${\rm Ext}_R^1(M,N)=0$ for all $N$ in the class of $GV$-torsion-free $R$-modules with the property that ${\rm Ext}^k_R(T,N)=0$ for all $w$-projective $R$-modules $T$ and all integers $k\geq1$. In this paper, we introduce and study some properties of weak $w$-projective modules. We use these modules to characterise some classical rings. For example, we will prove that a ring $R$ is a $DW$-ring if and only if every weak $w$-projective is projective; $R$ is a von Neumann regular ring if and only if every FP-projective module is weak $w$-projective if and only if every finitely presented $R$-module is weak $w$-projective; and $R$ is $w$-semi-hereditary if and only if every finite type submodule of a free module is weak $w$-projective if and only if every finitely generated ideal of $R$ is weak $w$-projective.</p>}, journal={New Zealand Journal of Mathematics}, author={Assaad, Refat Abdelmawla Khaled}, year={2024}, month={Jun.}, pages={43–52} }