Abstract
We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.
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