$n$-${\rm gr}$-coherent rings and Gorenstein graded modules

Graded Lie-Rinehart Algebras

“…On the other hand, gradings appear elsewhere in the theory of Lie algebras, for example in the Cartan decomposition of a finite-dimensional complex semisimple Lie algebra (see for instance [1,6,10,15,16,19,23]). Also, graded modules have attracted the attention of many researchers in the last years (see [2,4,5,8,28,31]). The concept of graded Lie-Rinehart algebra will allow us to study, under a unique structure, a graded Lie algebra which is also a module over a graded associative algebra.…”