A note on commutative baer rings
Journal of the Australian Mathematical Society | Published : 1972
In this note we study commutative Baer rings, uniting the abstract algebraic approach with the approach of  using minimal prime ideals. Some new characterisations of this class of rings are obtained, relations between the minimal prime ideals of a commutative Baer ring B and its algebra EB of idempotents are considered, and some results concerning the direct decomposition of commutative Baer rings are given. We then study Baer ideals, and finally state without proof a new construction of the Baer extension of a commutative semiprime ring.