University of MaraghehSahand Communications in Mathematical Analysis2322-580717320200701$n$-factorization Property of Bilinear Mappings1611734058410.22130/scma.2019.116000.696ENSedighehBarootkoobDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.0000-0003-1489-0975Journal Article20191019In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.http://scma.maragheh.ac.ir/article_40584_cbae0f5dc8463173efac6e2a2c9b9cae.pdf