Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/27776

 Title: Regular elements and Green's relations in Generalised Linear Transformation Semigroups Author(s): Gonçalves, Suzana MendesSullivan, R. P. Keywords: sandwich operationgeneralised linear transformationGreen's relationsregularunit-regularcompletely regulargeneralized 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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