A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal 2-algebras and crossed modules 3-Lie are interpreted by using lower degree groups.

(Minor corrections and additions have been made. The page layout has also been changed.) 0 Contents Contents 1 Abstract 2 Chapter 1: Constructions and Elementary Properties and Applications of Algebraic Extensions of Normed Algebras 3

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of al...

In this paper, we study universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras. We discuss $\alpha $-central extensions, the lifting automorphisms $-derivations to hom-Li

It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. In [JM08] a counterpart this result was studied in the set up differential matrix algebras, wherein Picard-Vessiot were constructed. article, we exhibit instances which extensions. some cases, relate existence splitting algebra to triviality its tensor powers, and show these orders div...