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arXiv · 2111.09938

Multiplicative summations into algebraically closed fields

Robert J. MacG. Dawson·Grant Molnar
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Abstract

In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-defined analogue to minimal polynomials for a series algebraic over a ring of series, the "scalar polynomial". When that ring is the domain of a summation $\mathfrak{S}$, we derive the related concepts of the $\mathfrak{S}$-minimal polynomial for a series, which is mapped by $\mathfrak{S}$ to a scalar polynomial. When the scalar polynomial for a series has the form $(t-a)^n$, $a$ is the unique value to which the series can be mapped by an extension of the original summation.

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Robert J. MacG. Dawson, Grant Molnar. 2021-11-18. Multiplicative summations into algebraically closed fields. https://arxiv.org/abs/2111.09938

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