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I wish to acknowledge fruitful discussions with G. Schiffels (see also the preprint by Dress & Schiffels, on Gröbner bases for monoid rings [2]).
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Ribenboim, P. Extension of Hironaka's standard basis theorem for generalized power series. Arch. Math 60, 436–439 (1993). https://doi.org/10.1007/BF01202308
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DOI: https://doi.org/10.1007/BF01202308