Genre
- Journal Article
We focus on matrix semigroups (and algebras) on which rank is commutable [rank(AB) = rank(BA)]. It is shown that in a number of cases (for example, in dimensions less than 6), but not always, commutativity of rank entails permutability of rank [rank(A(1)A(2)...A(n)) = rank(A(sigma(1))A(sigma(2))... A(sigma(n)))]. It is shown that a commutable-rank semigroup has a natural decomposition as a semi-lattice of semigroups that have a simpler structure. While it is still unknown whether commutativity of rank entails permutability of rank for algebras, the question is reduced to the case of algebras of nilpotents.
Colby Coll, Dept Math, Waterville, ME 04901 USA. Colby Coll, Dept Math & CS, Waterville, ME 04901 USA. Dalhousie Univ, Dept Math Stat & CS, Halifax, NS B3H 3J3, Canada. Univ Prince Edward Isl, Dept Math & CS, Charlottetown, PE C1A 4P3, Canada. W(TRUNCATED)
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SPRINGER-VERLAG
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Source type: Electronic(1)
Language
- English
Subjects
- Mathematics