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

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