Crabb, M. J., Duncan, J. and McGregor, C. M.
(2010)
On one-sided primitivity of Banach algebras.
*Proceedings of the Edinburgh Mathematical Society*, 53(01),
pp. 111-123.
(doi: 10.1017/S0013091508000783)

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Publisher's URL: http://dx.doi.org/10.1017/S0013091508000783

## Abstract

Let S be the semigroup With identity, generated by x and y, subject to y being invertible and yx = xy(2). We study two Banach algebra completions of the semigroup algebra. CS. Both completions are shown to be left-primitive and have separating families of irreducible infinite-dimensional right, modules. As an appendix, we offer an alternative proof that US is left-primitive but Hot right-primitive. We show further that. in contrast to the completions: every irreducible right module for US is finite dimensional and hence that US has a separating family of such modules.

Item Type: | Articles |
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Status: | Published |

Refereed: | Yes |

Glasgow Author(s) Enlighten ID: | McGregor, Dr Colin and Crabb, Dr Michael |

Authors: | Crabb, M. J., Duncan, J., and McGregor, C. M. |

College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |

Journal Name: | Proceedings of the Edinburgh Mathematical Society |

ISSN: | 0013-0915 |

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