A finiteness lemma,brauer's theorem and other iIrreducibility results |
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Authors: | M. Radjabalipour H. Radjavi |
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Affiliation: | 1. Mahani Mathematical Research Centre , University of Kerman , Kerman, Iran;2. Mathematics , Dalhousie University Halifax , Nova Scotia, B3H 3J5, Canada |
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Abstract: | A technical lemma is proved for certain semigroups of matrices. It has several applications to problems concerning irreducible semigroups satisfying spectral conditions, e.g., submultiplicativity of spectrum. It is also used to give extensions of the following theorem of Brauer's. If U is a finite group of complex matrices, so that for some integer m, every U in U, satisties Um =I then U has a representation over the cyclotomic field Q(ω), where ω is a primitive m-th root of unity. |
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Keywords: | Betti number Gotzmann number Hilbert function and polynomial Lex segment ideal Persistence index |
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