Some Properties of Local Cohomology Modules Defined by a Pair of Ideals

Let $R$ be a commutative Noetherian ring with identity and $I,J$ two ideals of $R.$ We introduce the concept of $(I,J)$-coweakly Laskerian modules and study their properties concerning to local cohomology modules with respect to a pair of ideals. We also study some properties of the local cohomology modules with support contained in $\mathrm{Max}(R)$ and the relationships on the weakly Artinianness of the modules $H^i_{I,J}(M)$ and $H^i_I(M)$.