Abstract
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 [Formula: see text] a derivative series of IGWAs, [Formula: see text], is attached where [Formula: see text] is an arbitrary ordinal. In general, all rings [Formula: see text] are distinct. A new construction of rings, the inner [Formula: see text]-extension of a ring, is introduced (where [Formula: see text] and [Formula: see text] are endomorphisms of a ring [Formula: see text] and [Formula: see text]).
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