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Rings Generated by Convergence Sets of Multidimensional Complete Field

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The convergence sets of a multidimensional complete field are those having the property that all power series over it converge when substituting an element of the maximal ideal for a variable. It is proved that a convergence set lies in the ring of integers if and only if it is contained in some convergence ring.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. I. Madunts

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  1. A. I. Madunts
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Correspondence to A. I. Madunts.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 500, 2021, pp. 149–157.

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Madunts, A.I. Rings Generated by Convergence Sets of Multidimensional Complete Field. J Math Sci 272, 444–449 (2023). https://doi.org/10.1007/s10958-023-06434-w

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  • DOI: https://doi.org/10.1007/s10958-023-06434-w

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