Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two dimensional perfect evolution algebras over domains   We will study evolution algebras $A$ which are free modules of dimension $2$
over domains. Furthermore, we will assume that these algebras are perfect, that
is $A^2=A$. We start by making some general considerations about algebras over
domains: they are sandwiched between a certain essential $D$-submodule and its
scalar extension over the field of fractions of the domain. We introduce the
notion of quasiperfect algebras and modify slightly the procedure to associate
a graph to an evolution algebra over a field given in \cite{ElduqueGraphs}.
Essentially, we introduce color in the connecting arrows, depending on a
suitable criterion related to the squares of the natural basis elements. Then
we classify the algebras under scope parametrizing the isomorphic classes by
convenient moduli.

21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph