@article { author = {Mousavi Mirkalai, Seyed Shahin and Hosseini, Naser and Ilaghi-Hosseini, Azadeh}, title = {On general closure operators and quasi factorization structures}, journal = {Categories and General Algebraic Structures with Applications}, volume = {14}, number = {1}, pages = {39-80}, year = {2021}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.14.1.39}, abstract = {In this article the notions of quasi mono (epi) as a generalization of mono (epi), (quasi weakly hereditary) general closure operator $\mathbf{C}$ on a category $\mathcal{X}$ with respect to a class $\mathcal{M}$ of morphisms, and quasi factorization structures in a category $\mathcal{X}$ are introduced. It is shown that under certain conditions, if $(\mathcal{E}, \mathcal{M})$ is a quasi factorization structure in $\mathcal{X}$, then $\mathcal{X}$ has a quasi right $\mathcal{M}$-factorization structure and a quasi left $\mathcal{E}$-factorization structure. It is also shown that for a quasi weakly hereditary and quasi idempotent QCD-closure operator with respect to a certain class $\mathcal{M}$, every quasi factorization structure $(\mathcal{E}, \mathcal{M})$ yields a quasi factorization structure relative to the given closure operator; and that for a closure operator with respect to a certain class $\mathcal{M}$, if the pair of classes of quasi dense and quasi closed morphisms forms a quasi factorization structure, then the closure operator is both quasi weakly hereditary and quasi idempotent. Several illustrative examples are provided.}, keywords = {Quasi mono (epi),quasi (right,left) factorization structure,(quasi weakly hereditary,quasi idempotent) general closure operator}, url = {https://cgasa.sbu.ac.ir/article_87435.html}, eprint = {https://cgasa.sbu.ac.ir/article_87435_57be9bc0e817ada7c5f3c927f59226c3.pdf} }