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TitleRegular elements and Green's relations in Generalised Linear Transformation Semigroups
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
Keywordssandwich operation
generalised linear transformation
Green's relations
completely regular
generalized transformation
Issue date2013
PublisherSoutheast Asian Mathematical Society
JournalSoutheast 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.
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Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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