TY - JOUR ID - 87435 TI - On general closure operators and quasi factorization structures JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Mousavi Mirkalai, Seyed Shahin AU - Hosseini, Naser AU - Ilaghi-Hosseini, Azadeh AD - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran AD - Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran AD - Department of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of Kerman Y1 - 2021 PY - 2021 VL - 14 IS - 1 SP - 39 EP - 80 KW - Quasi mono (epi) KW - quasi (right KW - left) factorization structure KW - (quasi weakly hereditary KW - quasi idempotent) general closure operator DO - 10.29252/cgasa.14.1.39 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_87435.html L1 - https://cgasa.sbu.ac.ir/article_87435_57be9bc0e817ada7c5f3c927f59226c3.pdf ER -