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The algebraic structure of linearly recursive sequences under hadamard product


We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.

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Supported in part by NSF Grant DMS 870-1085.

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Larson, R.G., Taft, E.J. The algebraic structure of linearly recursive sequences under hadamard product. Israel J. Math. 72, 118–132 (1990).

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  • Hopf Algebra
  • Algebraic Structure
  • Algebra Homomorphism
  • Zero Divisor
  • Hadamard Product