Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/16144

TitleThe ideal structure of semigroups of linear transformations with lower bounds on their nullity or defect
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
KeywordsBi-ideal
Quasi-ideal
Linear transformation semigroup
Maximal regular subsemigroup
Maximal right cancellative subsemigroup
Issue dateMar-2010
PublisherWorld Scientific and Engineering Academy and Society (WSEAS)
JournalAlgebra Colloquium
Abstract(s)Suppose V is an infinite-dimensional vector space and let T(V ) denote the semigroup (under composition) of all linear transformations of V . In this paper, we study the semigroup OM(p, q) consisting of all alpha in T(V ) for which dim ker >= q and the semigroup OE(p, q) of all alpha in T(V ) for which codim ran >= q, where dim V = p >= q >= aleph0. It is not difficult to see that OM(p, q) and OE(p, q) are a right and a left ideal of T(V ), respectively, and using these facts we show that they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Also, we describe the Green’s relations and the two-sided ideals of each semigroup, and we determine its maximal regular subsemigroup. Finally, we determine some maximal right cancellative subsemigroups of OE(p, q).
TypeArticle
URIhttp://hdl.handle.net/1822/16144
DOI10.1142/S1005386710000131
ISSN1005-3867
Publisher versionhttp://www.worldscinet.com/ac/17/1701/S10053867101701.html
Peer-Reviewedyes
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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