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Annihilating and power-commuting generalized skew derivations on Lie ideals in prime rings

Vincenzo de Filippis (2016)

Czechoslovak Mathematical Journal

Let R be a prime ring of characteristic different from 2 and 3, Q r its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R . An additive map D : R → R is called an α -derivation (or a skew derivation) on R if D ( x y ) = D ( x ) y + α ( x ) D ( y ) for all x , y ∈ R . An additive mapping F : R → R is called a generalized α -derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F ( x y ) = F ( x ) y + α ( x ) D ( y ) for all x , y ∈ R . We prove that, if F ...

Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang, Xiaoming Li (2023)

Czechoslovak Mathematical Journal

Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.

Annihilators of skew derivations with Engel conditions on prime rings

Taylan Pehlivan, Emine Albas (2020)

Czechoslovak Mathematical Journal

Let R be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring Q , C the extended centroid of R and a ∈ R . Suppose that δ is a nonzero σ -derivation of R such that a [ δ ( x n ) , x n ] k = 0 for all x ∈ R , where σ is an automorphism of R , n and k are fixed positive integers. Then a = 0 .

Applications of spinor class fields: embeddings of orders and quaternionic lattices

Luis Arenas-Carmona (2003)

Annales de l'Institut Fourier

We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.

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