10 research outputs found
Regular elements and Green's relations in Generalised Linear Transformation Semigroups
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 , then P(V,W) is a so-called `generalised semigroup' of linear transformations under the `sandwich operation': , for each . We denote this semigroup by 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 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 and characterise when these semigroups satisfy certain regularity conditions.Fundação para a Ciência e a Tecnologia (FCT