Counterexamples on baer rings

摘要

In this paper we give counterexamples to the following questions: (1) Are commutative reduced rings Baer?, (2) Are commutative von Neumann regular rings Baer?, (3) Are reduced rings with center Baer also Baer?, and (4) Are prime Pi-rings Baer? Moreover we consider some conditions under which the answers of them are affirmative.