Multiplicative summations into algebraically closed fields
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 welldefined 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 $(ta)^n$, $a$ is the unique value to which the series can be mapped by an extension of the original summation.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.09938
 Bibcode:
 2021arXiv211109938M
 Keywords:

 Mathematics  Commutative Algebra;
 40C99 (Primary);
 12E05;
 13F25;
 16W60 (Secondary)
 EPrint:
 19 pages