Lie and Jordan structures in simple associative rings

Lie and Jordan Structures in Simple, Associative Rings

Jordan structures and non-associative geometry

We give an overview over constructions of geometries associated to Jordan structures (algebras, triple systems and pairs), featuring analogs of these constructions with the Lie functor on the one hand and with the approach of noncommutative geometry on the other hand.

Jordan Gradings on Exceptional Simple Lie Algebras

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.

Lie and Jordan Structure in Simple Γ− Regular Ring

In this paper, we study Lie and Jordan Structure in Simple Γ− Regular Ring of characteristic not equal to two. Some Properties of these Γ− Regular Ring are determined.

On One-sided Lie Nilpotent Ideals of Associative Rings

We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...