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Rota's Classification Problem, rewriting systems and Gröbner-Shirshov bases (1601.04254v1)
Published 17 Jan 2016 in math.RA and math.CT
Abstract: In this paper we revisit Rota's Classification Problem on classifying algebraic identities for linear operator. We reformulate Rota's Classification Problem in the contexts of rewriting systems and Gr\"obner-Shirshov bases, through which Rota's Classification Problem amounts to the classification of operators, given by their defining operator identities, that give convergent rewriting systems or Gr\"obner-Shirshov bases. Relationship is established between the reformulations in terms of rewriting systems and that of Gr\"obner-Shirshov bases. We provide an effective condition that gives Gr\"obner-Shirshov operators and obtain a new class of Gr\"obner-Shirshov operators.