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De Nugis Groebnerialium 7: Janet, Gerdt, Tamari

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Abstract

In this paper we discuss the theory of involutive divisions and bases, generalizing the setting to twisted polynomials over a PIR. We also give an insight about the context of Tamari rings.

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Notes

  1. This of course implies that the arithmetics of both \({\mathcal A}\) and R can be simply performed by Buchberger reduction and justifies the notion of being effectively given.

  2. The interested reader can also see [18] for the study of involutive bases over the quotient ring of the commutative polynomial ring over a field modulo an ideal.

  3. The term \(x_1^ix_2^j\) corresponds to (i, j); dots are terms in the ideal, diamonds terms in the escalier.

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Authors and Affiliations

  1. Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy

    Michela Ceria

  2. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy

    Ferdinando Mora

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  1. Michela Ceria
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  2. Ferdinando Mora
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Ceria, M., Mora, F. De Nugis Groebnerialium 7: Janet, Gerdt, Tamari. Math.Comput.Sci. 16, 29 (2022). https://doi.org/10.1007/s11786-022-00549-0

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