J. Aust. Math. Soc.  80 (2006), 263-272
On semiprime segments of rings

R. Mazurek
  Faculty of Computer Science
  Bialystok Technical University
  Wiejska 45A
  15-351 Bialystok
G. Törner
  Institut für Mathematik
  Fakultät 4
  Universität Duisburg-Essen
  Campus Duisburg
  47048 Duisburg

A semiprime segment of a ring $R$ is a pair $P_2 \subset P_1$ of semiprime ideals of $R$ such that $\bigcap I^n \subseteq P_2$ for all ideals $I$ of $R$ with $P_2 \subset I \subset P_1$. In this paper semiprime segments with $P_1$ a comparizer ideal are classified as either simple, exceptional, or archimedean, extending to several classes of rings a classification known for right chain rings. These three types of semiprime segments are also characterized in terms of the pseudo-radical.
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