Narrow Results

The aim of the paper is to introduce a new class of rings — the inner generalized Weyl algebras (IGWA) — and to give simplicity criteria for them. For each IGWA $A$ a derivative series of IGWAs, $A\to A^{\prime }\to A^{″}\to \cdots \to A^{(\alpha )}\to \cdots$, is attached where $\alpha$ is an arbitrary ordinal. In general, all rings $A^{(\alpha )}$ are distinct. A new construction of rings, the inner $(\sigma ,\tau ,a)$-extension of a ring, is introduced (where $\sigma$ and $\tau$ are endomorphisms of a ring $D$ and $a\in D$).