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We identify some situations where mappings related to left centralizers, derivations and generalized $(α, β)$ -derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation $T$ , of a semiprime ring $R$ the mapping $ψ R \to R$ defined by $ψ (x) = T (x) x - x T (x)$ for all $x \in R$ is a free action. We also show that for a generalized $(α, β)$ -derivation $F$ of a semiprime ring $R,$ with associated $(α, β)$ -derivation $d,$ a dependent element $a$ of $F$ is also a dependent element of $α + d .$ Furthermore, we prove that for a centralizer $f$ and...

Fully rigid systems of modules

A. L. S. Corner (1989)

Rendiconti del Seminario Matematico della Università di Padova

Galois actions on rings and finite Galois coverings.

M. Auslander, I. Reiten, S.O. Smalo (1989)

Mathematica Scandinavica

Galois extensions as functors of comodules.

K.-H. Ulbrich (1987)

Manuscripta mathematica

Generalizations of Hopfian and co-Hopfian modules.

Wang, Yongduo (2005)

International Journal of Mathematics and Mathematical Sciences

Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra $E n d_{R} A$ of the R-module $_{R} A$ , taking any a ∈ A to the right multiplication $a_{r} \in E n d_{R} A$ by a, is an isomorphism of algebras. In this case $_{R} A$ is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...

Generators for the divided powers algebra of an algebra and trace identities

Dieter Ziplies (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Global Dimension of Differential Operator Rings. IV - Simple Modules.

Kenneth R. Goodearl (1989)

Forum mathematicum

Grothendieck groups of invariant ring: linear actions of finite groups.

Martin Lorenz, Kennth A. Brown (1996)

Mathematische Zeitschrift

Group graded rings and smash products

C. Năstăsescu, N. Rodinò (1985)

Rendiconti del Seminario Matematico della Università di Padova

Groups of periods for arbitrary maps on groups.

Bonciocat, N.C., Zaharescu, A. (2005)

Acta Mathematica Universitatis Comenianae. New Series

Groups of simple algebras

Moss E. Sweedler (1974)

Publications Mathématiques de l'IHÉS

Higher order derivations of modules

Ribenboim, P. (1980)

Portugaliae mathematica

Hochschild homology and cohomology of generalized Weyl algebras

Marco A. Farinati, Andrea L. Solotar, Mariano Suárez-Álvarez (2003)

Annales de l’institut Fourier

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, $𝒰 (𝔰 𝔩_{2})$ , primitive quotients of $𝒰 (𝔰 𝔩_{2})$ , and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula–Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generators of the group of automorphisms of a generalized Weyl...

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