Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On local linear convexity generalized to commutative algebras   A commutative associative algebra A with an identity over the field of real
numbers which has a basis, where all elements are invertible, is considered in
the work. Moreover, among matrixes consisting of the structure constants of A,
there is at least one that is non-degenerate. The notion of linearly convex
domains in the multi-dimensional complex space and some of their properties are
generalized to the space that is the Cartesian product of n algebras A. Namely,
the separate necessary and sufficient conditions of the local A-linear
convexity of domains with smooth boundary in the space are obtained in terms of
nonnegativity and positivity of formal quadratic differential form in A,
respectively.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con