Abstract
The class of commutative rings known as Baer rings was first discussed by J. Kist [4], where many interesting properties of these rings were established. Not necessarily commutative Baer rings had previously been studied by I. Kaplansky [3], and by R. Baer himself [1]. In this note we show that commutative Baer rings, which generalize Boolean rings and p-rings, satisfy the Birkhoff conditions for a variety. Next we give a set of equations characterising this variety involving + and * as binary operations, – and as unary operations, and 0 as nullary operation. Finally we describe Baer-subdirectly irreducible commutative Baer rings and state the appropriate representation theorem.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. [5] Speed T. P. , ‘A note on commutative Baer rings’ J. Aust. Math. Soc. (to appear).
2. Minimal Prime Ideals in Commutative Semigroups
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