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Статья

On Hasse–Schmidt rings and module algebras

Journal of Pure and Applied Algebra. 2013. Vol. 217. No. 7. P. 1305-1315.
Heiderich F.

Recently,Moosa and Scanlon introduced(iterative)Hasse–Schmidt systems D and,given such a Hasse–Schmidt system, they defined (iterative)D-rings, generalizing rings with higher derivation as introduced by Hasse and Schmidt in 1937. We show that there is a bijection between Hasse–Schmidt systems D and cocommutative coalgebras D. For a given Hasse–Schmidt system D with associated coalgebra D we show that D-ring are in bijection to algebras with a D-measuring on them.Under these correspondences iterative Hasse–Schmidt systems D correspond to cocommutative bialgebras D and iterative В-rings correspond to D-module algabras.