Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-dimensional Einstein numbers and associativity   In this paper, we deal with generalizations of real Einstein numbers to
various spaces and dimensions. We search operations and their properties in
generalized settings. Especially, we are interested in the generalized
operation of hyperbolic addition to more-dimensional spaces, which is
associative and commutative. We extend the theory to some abstract spaces,
especially to Hilbert-like ones. Further, we bring two different
two-dimensional generalizations of Einstein numbers and study properties of
new-defined operations -- mainly associativity, commutativity, and distributive
laws.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys