The product formula for evaluating products of skew polynomials is used to construct a class of rings. As an application, we present a method of evaluating quotients of skew polynomials.
We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via a cohomology theory.
In this paper, we introduce the notion of curved 𝒪-operator systems as a generalization of T. Brzeziński’s (curved) Rota-Baxter systems, and then investigate their relations with 𝒪-operator systems, (tri)dendriform systems, pre-Lie algebras, associative Yang-Baxter pairs and quasitriangular covariant bialgebras.
For a module having a complete injective resolution, we define a stable version of local cohomology. This gives a functor to the stable category of Gorenstein injective modules. We show that in many ways this functor behaves like the usual local cohomology functor. Our main result is that when there is only one nonzero local cohomology module, there is a strong connection between that module and the stable local cohomology module; in fact, the latter gives a Gorenstein injective approximation of the former.