Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicative summations into algebraically closed fields   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.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph