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Title: | Regular elements and Green's relations in Generalised Linear Transformation Semigroups |

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

Keywords: | sandwich operation generalised linear transformation Green's relations regular unit-regular completely regular generalized transformation |

Issue date: | 2013 |

Publisher: | Southeast Asian Mathematical Society |

Journal: | Southeast Asian Bulletin of Mathematics |

Abstract(s): | If V and W are vector spaces over the same field, we let P(V,W) denote the set of all partial linear transformations from V into W (that is, all linear mappings whose domain and range are subspaces of V and W, respectively). If $\theta\in P(W,V)$, then P(V,W) is a so-called `generalised semigroup' of linear transformations under the `sandwich operation': $\alpha *\beta=\alpha\circ\theta\circ\beta$, for each $\alpha,\beta\in P(V,W)$. We denote this semigroup by $P(V,W,\theta)$ and, in this paper, we characterise Green's relations on it: that is, we study equivalence relations which determine when principal left (or right, or 2-sided) ideals in $P(V,W,\theta)$ are equal. This is related to a problem raised by Magill and Subbiah in 1975. We also discuss the same idea for important subsemigroups of $P(V,W,\theta)$ and characterise when these semigroups satisfy certain regularity conditions. |

Type: | Article |

URI: | http://hdl.handle.net/1822/27776 |

DOI: | 10.1142/S179355711350006X |

ISSN: | 0129-2021 |

Publisher version: | www.seams-bull-math.ynu.edu.cn |

Peer-Reviewed: | yes |

Access: | Restricted access (UMinho) |

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

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green_generallintransf.pdf Restricted access | Documento único | 154,35 kB | Adobe PDF | View/Open |