Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/11152

 Title: The ideal structure of semigroups of linear transformations with upper bounds on their nullity or defect Author(s): Gonçalves, Suzana MendesSullivan, R. P. Keywords: Bi-idealQuasi-idealLinear transformation semigroupMaximal regularMaximal 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)

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