The module of linear recurring sequences over a commutative ring R can be considered as a Hopf algebra dual to the polynomial Hopf algebra over R. Under this approach, some notions and operations from the Hopf algebra theory have an interesting interpretation in terms of linear recurring sequences. Generalizations are also considered: linear recurring bisequences, sequences over modules, and k-sequences.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 113–148, 2003.
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Kurakin, V.L. Hopf Algebras of Linear Recurring Sequences over Rings and Modules. J Math Sci 128, 3402–3427 (2005). https://doi.org/10.1007/s10958-005-0279-8
- Hopf Algebra
- Commutative Ring
- Algebra Theory
- Interesting Interpretation