Abstract
In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series.
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