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Title: | The ideal structure of semigroups of linear transformations with upper bounds on their nullity or defect |

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

Keywords: | Bi-ideal Quasi-ideal Linear transformation semigroup Maximal regular Maximal right simple |

Issue date: | 2009 |

Publisher: | Taylor and Francis |

Journal: | Communications in Algebra |

Citation: | "Communications in Algebra". ISSN 0092-7872 . 37:7 (2009) 2522-2539.. |

Abstract(s): | Suppose $V$ is a vector space with ${\rm dim} V=p\geq q\geq\aleph_0$, and let $T(V)$ denote the semigroup (under composition) of all linear transformations of $V$. For each $\alpha\in T(V)$, let ${\rm ker}\alpha$ and ${\rm ran}\alpha$ denote the `kernel' and the `range' of $\alpha$, and write $n(\alpha)={\rm dim}{\rm ker}\alpha$ and $d(\alpha)={\rm codim}{\rm ran}\alpha$. In this paper, we study the semigroups $AM(p,q) =\{\alpha\in T(V):n(\alpha)<q\}$ and $AE(p,q) =\{\alpha\in T(V):d(\alpha)<q\}$. First, we determine whether they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Then, for each semigroup, we describe its maximal regular subsemigroup, and we characterise its Green's relations and (two-sided) ideals. As a precursor to further work in this area, we also determine all the maximal right simple subsemigroups of $AM(p,q)$. |

Type: | Article |

URI: | http://hdl.handle.net/1822/11152 |

DOI: | 10.1080/00927870802622932 |

ISSN: | 0092-7872 |

Publisher version: | http://www.informaworld.com |

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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upperbounds.pdf | Documento principal | 171,49 kB | Adobe PDF | View/Open |