Israel Journal of Mathematics

, Volume 72, Issue 1–2, pp 118–132 | Cite as

The algebraic structure of linearly recursive sequences under hadamard product

  • Richard G. Larson
  • Earl J. Taft


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.


Hopf Algebra Algebraic Structure Algebra Homomorphism Zero Divisor Hadamard Product 
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Copyright information

© The Weizmann Science Press of Israel 1990

Authors and Affiliations

  • Richard G. Larson
    • 1
  • Earl J. Taft
    • 2
  1. 1.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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