Crossed Modules of Hom-Leibniz-Rinehart Algebras

On the basis of previous studies, Hom-noncommutative algebra is further studied. Firstly, the definition of Hom-action on Hom-Leibniz-Rinehart algebra is given. Secondly, on the directsum of Hom-Leibniz-Rinehart algebras and Hom-Leibniz A-algebras, it is defined that the left anchor, right anchor and endomorphism are semi-direct products, and it is proved that there is a one-to-one correspondence between their actions and Hom-Leibniz-Rinehart-algebras. Finally, the cross module of Hom-Leibniz-Rinehart algebra is defined, and the corresponding relationship between cross module and algebraic homomorphism is proved.