Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The Jacobson radical of a band ring

W. D. Munna1

a1 Department of Mathematics, University of Glasgow, Glasgow G12 8QW

A band is a semigroup in which every element is idempotent. In this note we give an explicit description of the Jacobson radical of the semigroup ring of a band over a ring with unity. It is shown, further, that this radical is nil if and only if the Jacobson radical of the coefficient ring is nil. For the particular case of a normal band (see below for the definition) the Jacobson radical of the band ring is nilpotent if and only if the Jacobson radical of the coefficient ring is nilpotent; but this result does not extend to arbitrary bands.

(Received March 08 1988)