Semigroups of linear endomorphisms closed under conjugation |
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| Authors: | João Araújo Fernando C Silva |
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| Institution: | 1. Centro de álgebra , Universidade de Lisboa , Av. Prof. Gama Pinto 2, Lisboa, 1649-003, Portugal E-mail: mjoao@lmc.fc.ul.pt;2. Departamento de Matemática , Faculdade de Ciências Universidade de Lisboa , Lisboa, 1749-016, Portugal E-mail: fcsilva@fc.ul.pt |
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| Abstract: | Let a,b be singular endomorphisms of a. finite dimensional vector space V and denote by S a the semigroup generated by all the elements g -1ag, where g?Aut(V).The aim of this paper is to prove that b?S a if and only if rank(b) ≥ rank(a). |
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