@article { author = {Heidarian, Zahra}, title = {The existence totally reflexive covers}, journal = {Algebraic Structures and Their Applications}, volume = {6}, number = {2}, pages = {81-86}, year = {2019}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2019.1486}, abstract = {Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$\varphi:C \rightarrow M$ such that $C$ is finitely generated and the projective dimension of $\Ker\varphi$ is finite and $\varphi$ is surjective.}, keywords = {Cover,Precover,Gorenstein projective,totally reflexive}, url = {https://as.yazd.ac.ir/article_1486.html}, eprint = {https://as.yazd.ac.ir/article_1486_b92b829ea109a8df9db22610a0de01e2.pdf} }