Subalgebras of matrix algebras generated by companion matrices |
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Authors: | N.H. Guersenzvaig |
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Affiliation: | a Av. Corrientes 3985 6A, (1194) Buenos Aires, Argentina b Department of Mathematics and Statistics, University of Regina, Saskatchewan, Canada |
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Abstract: | Let f,g∈Z[X] be monic polynomials of degree n and let C,D∈Mn(Z) be the corresponding companion matrices. We find necessary and sufficient conditions for the subalgebra Z〈C,D〉 to be a sublattice of finite index in the full integral lattice Mn(Z), in which case we compute the exact value of this index in terms of the resultant of f and g. If R is a commutative ring with identity we determine when R〈C,D〉=Mn(R), in which case a presentation for Mn(R) in terms of C and D is given. |
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Keywords: | 16S50 |
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