Multiplicative summations into algebraically closed fields
| Autor: | Dawson, Robert J. MacG., Molnar, Grant |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 19 pages |
| Databáze: | arXiv |
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