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TitleThe ideal structure of semigroups of linear transformations with lower bounds on their nullity or defect
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
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).
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Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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