The algebraic structure of linearly recursive sequences under hadamard product
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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.
KeywordsHopf Algebra Algebraic Structure Algebra Homomorphism Zero Divisor Hadamard Product
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- 1.M. F. Atyah and I. G. Macdonald,Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969.Google Scholar
- 6.A. J. van der Poorten,Some facts that should be better known, especially about rational functions, inNumber Theory and Applications (R. A. Mollin, ed.), Kluwer Acad. Publ., Dordrecht, 1989.Google Scholar
- 9.M. Sweedler,Hopf Algebras, Benjamin, New York, 1969.Google Scholar