Ebook: Ilaghi-Hosseini A. On General Closure Operators and Quasi Factorization Structures

New York.: Ithaca, Cornell University Library, 22 Dec. 2014, p.p.: 1-21, eBook, English.
{Free Published: E-Print Cornell University Library (arXiv:1412.6930v1 [math.CT] 22 Dec 2014)}.
Abstract.
In this article the notions of (quasi weakly hereditary) general closure operator C on a category X with respect to a class M of morphisms, and quasi factorization structures in a category X are introduced. It is shown that under certain conditions, if (E , M) is a quasi factorization structure in X , then X has quasi right M-factorization structure and quasi left 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 M, every quasi factorization structure (E , M) yields a quasi factorization structure relative to the given closure operator; and that for a closure operator with respect to a certain class 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 furnished.Contents.
Introduction.
General Closure Operators.
Quasi idempotent and quasi weakly hereditary closure operators.
Quasi factorization structures.
References.