Vol. 50, No. 1, 1974

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Two characterizations of commutative Baer rings

Joseph Edmund Kist

Vol. 50 (1974), No. 1, 125–134
Abstract

A commutative ring A is called a Baer ring if the annihilator of each element in A is the principal ideal generated by an idempotent. It is shown that the following three conditions on a semiprime commutative ring A with identity are equivalent: (1) A is a Baer ring, (2) the mapping Q Q E is a homeomorphism of Min SpecA with the Boolean space of the Boolean algebra E of idempotents in A, (3) Min Spec A is a retract of SpecA.

Mathematical Subject Classification 2000
Primary: 13A15
Milestones
Received: 29 September 1972
Published: 1 January 1974
Authors
Joseph Edmund Kist