Journal article

A note on commutative baer rings

TP Speed, MW Evans

Journal of the Australian Mathematical Society | Published : 1972

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.

University of Melbourne Researchers

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