Inner generalized Weyl algebras and their simplicity criteria.

The aim of the paper is to introduce a new class of rings — the <italic>inner generalized Weyl algebras</italic> (IGWA) — and to give simplicity criteria for them. For each IGWA A a derivative series of IGWAs, A → A′→ A″ →⋯ → A(α) →⋯, is attached where α is an arbitrary ordinal. In general, all rings A(α) are distinct. A new construction of rings, the <italic>inner</italic> (σ,τ,a)<italic>-extension</italic> of a ring, is introduced (where σ and τ are endomorphisms of a ring D and a ∈ D). [ABSTRACT FROM AUTHOR]