فهرست نشریات علمی دسترسی آزاد ایران

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.