Rings of very strong finite type

Abstract

The SFT (for strong finite type) condition was introduced by J. Arnold in the context of studying the condition for formal power series rings to have finite Krull dimension. In the context of commutative rings, the SFT property is a near-Noetherian property that is necessary for a ring of formal power series to have finite Krull dimension behavior. In this paper, we explore a specialization (and in some sense a more natural) variant of the SFT property that we dub the VSFT (for very strong finite type) property. We explore some of the fundamental properties of VSFT ideals and rings and compare and contrast with the known SFT condition.