An analogue of Amitsur's property for the ring of pseudo-differential operators

TL;DR

This paper extends Amitsur's property to pseudo-differential operator rings with derivations, providing new insights into their radical structure and prime radical characterization.

Contribution

It introduces an analogue of Amitsur's property for pseudo-differential operator rings with derivations, a novel theoretical development.

Findings

Amitsur's property analogue holds for pseudo-differential operator rings

Characterization of the prime radical of R((x^{-1}; δ))

Enhanced understanding of radical structures in differential operator rings

Abstract

Let R be a ring with a derivation \delta. In this paper, we prove that an analogue of Amitsur's property holds for left T-nilpotent radideals of pseudo-differential operator rings R((x^{-1}; \delta)), where R is a delta-compatible ring. As a direct consequence of this fact, we obtain an alternative characterization of the prime radical of R((x^{-1}; \delta)).