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Title: | Baer-Levi semigroups of linear transformations |

Author(s): | Gonçalves, Suzana Mendes Sullivan, R. P. |

Keywords: | Semigroups of linear transformations |

Issue date: | 2004 |

Publisher: | Royal Society of Edinburgh |

Journal: | Proceedings of the Royal Society of Edinburgh Section A-Mathematics |

Citation: | “Proceedings section A : mathematics - The Royal Society of Edinburgh”. ISSN 0308-2105. 134:3 (2004) 477-499. |

Abstract(s): | Given an infinite-dimensional vector space V, we consider the semigroup GS(m,n) of all injective linear transformations of V into itself with defect n, where n is an infinite cardinal less or equal than m, the dimension of V. This is a linear version of the well-known Baer-Levi semigroup BL(p,q) defined on an infinite set X with cardinal p and where q is an infinite cardinal less or equal than p. We show that, although the basic properties of GS(m,n) are the same as those of BL(p,q), the two semigroups are never isomorphic. We also determine all left ideals of GS(m,n) and some of its maximal subsemigroups: in this, we follow previous work on BL(p,q) by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984). |

Type: | Article |

URI: | http://hdl.handle.net/1822/1825 |

DOI: | 10.1017/S0308210500003309 |

ISSN: | 0308-2105 1473-7124 |

Peer-Reviewed: | yes |

Access: | Open access |

Appears in Collections: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |

Files in This Item:

File | Description | Size | Format | |
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linearBLsgp.pdf | 199,77 kB | Adobe PDF | View/Open |