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The Jacobson radical of a band ring

  • W. D. Munn (a1)
Abstract

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.

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[5] D. B. McAlister . Representations of semigroups by linear transformations II. Sernigroup Forum 2 (1971), 283320.

[7] M. L. Teply , E. G. Turman and A. Quesada . On semisimple semigroup rings. Proc. Amer. Math. Soc. 79 (1980), 157163.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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