Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras
L. A. Bokut, Yuqun Chen, Zerui Zhang · Journal of Algebra and Its Applications · 2015
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.