Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Every synaptic algebra has the monotone square root property   A synaptic algebra is a common generalization of several ordered algebraic
structures based on algebras of self-adjoint operators, including the
self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic
algebra A has the monotone square property, i.e., if a and b are positive
elements, then if a is less or equal than b, then the square root of a is less
or equal than the square root of b.

33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph