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

TitleThe ideal structure of semigroups of linear transformations with upper bounds on their nullity or defect
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
KeywordsBi-ideal
Quasi-ideal
Linear transformation semigroup
Maximal regular
Maximal right simple
Issue date2009
PublisherTaylor and Francis
JournalCommunications 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 $AM(p,q) =\{\alpha\in T(V):n(\alpha)<q\}$ and $AE(p,q) =\{\alpha\in T(V):d(\alpha)<q\}$. First, we determine whether they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Then, for each semigroup, we describe its maximal regular subsemigroup, and we characterise its Green's relations and (two-sided) ideals. As a precursor to further work in this area, we also determine all the maximal right simple subsemigroups of $AM(p,q)$.
TypeArticle
URIhttp://hdl.handle.net/1822/11152
DOI10.1080/00927870802622932
ISSN0092-7872
Publisher versionhttp://www.informaworld.com
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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