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Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring

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Associative and Non-Associative Algebras and Applications (MAMAA 2018)

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Abstract

Commutative and non commutative Gröbner–Shirshov bases were first studied over fields and after extended to some particular rings. In theses works, the monomials are in a monoid. Recently, Bokut and al. gave a new extension of Gröbner–Shirshov bases over a field by choosing the monomials in a semi-ring rather in a monoid. In this paper, we study Gröbner–Shirshov bases where the monomials are in a semi-ring and the coefficients are in a noetherian valuation ring and we establish the relation between weak and strong Gröbner bases.

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Acknowledgements

This work was partially supported by CEA-MITIC (Centre d’Excellence Africain en Mathématiques, Informatique et TIC).

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Correspondence to Yatma Diop .

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Diop, Y., Mesmoudi, L., Sow, D. (2020). Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring. In: Siles Molina, M., El Kaoutit, L., Louzari, M., Ben Yakoub, L., Benslimane, M. (eds) Associative and Non-Associative Algebras and Applications. MAMAA 2018. Springer Proceedings in Mathematics & Statistics, vol 311. Springer, Cham. https://doi.org/10.1007/978-3-030-35256-1_11

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