On Amitsur rings

Abstract

In this note, we introduce (hereditary) Amitsur rings and give examples of (hereditary) Amitsur rings. We construct radicals T and T_S. We also find radicals in which every prime ring is a hereditary Amitsur ring and radicals in which every prime ring is not a hereditary Amitsur ring. We give characterizations for (hereditary) Amitsur rings and prove that the semisimple class ST_S is polynomial extensible. We show that all zero rings are Amitsur rings and all Baer radical rings are hereditary Amitsur rings.

Mathematics Subject Classification (2010): 16N80.

Keywords: Amitsur rings, hereditary Amitsur rings, radicals, radicals with the Amitsur property