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    Fountain, John 2010. The work of Douglas Munn and its legacy. Semigroup Forum, Vol. 81, Issue. 1, p. 2.


    Kelarev, A. V. Yearwood, J. L. Watters, P. Wu, X. Abawajy, J. H. and Pan, L. 2010. Internet security applications of the Munn rings. Semigroup Forum, Vol. 81, Issue. 1, p. 162.


    Kelarev, A. V. 1996. ON THE STRUCTURE OF THE JACOBSON RADICAL OF GRADED RINGS. Quaestiones Mathematicae, Vol. 19, Issue. 1-2, p. 331.


    Kelarev, A. V. and Okniński, J. 1995. On group graded rings satisfying polynomial identities. Glasgow Mathematical Journal, Vol. 37, Issue. 02, p. 205.


    Kelarev, A. V. 1994. Radicals of semigroup rings of commutative semigroups. Semigroup Forum, Vol. 48, Issue. 1, p. 1.


    KELAREV, A.V. 1993. Theory of Radicals.


    Kelarev, A.V. 1992. Radicals of graded rings and applications to semigroup rings. Communications in Algebra, Vol. 20, Issue. 3, p. 681.


    Kelarev, A. V. 1990. On the Jacobson radical of semigroup rings of commutative semigroups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 108, Issue. 03, p. 429.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 105, Issue 2
  • March 1989, pp. 277-283

The Jacobson radical of a band ring

  • W. D. Munn (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100067761
  • Published online: 24 October 2008
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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