Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 5 1 2020 06 01 Regularity of Bounded Tri-Linear Maps and the Fourth Adjoint of a Tri-Derivation منظمی نگاشت های سه خطی کران دار و الحاقی چهارم از سه اشتقاق 51 65 166 10.22128/gadm.2020.358.1028 EN Abotaleb Sheikhali payame noor univercity Ali Ebadian Payame Noor Univercity Kazem Haghnejad Azar mohagheghe ardabili Journal Article 2020 02 24 In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation. https://ansne.du.ac.ir/article_166_e2827d0a9621a936e9b960761cf28f77.pdf