Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A scoop from groups: Equational foundations for loops   Groups are usually axiomatized as algebras with an associative binary
operation, a two-sided neutral element, and with two-sided inverses. We show in
this note that the same simplicity of axioms can be achieved for some of the
most important varieties of loops. In particular, we investigate loops of
Bol-Moufang type in the underlying variety of magmas with two-sided inverses,
and obtain "group-like" equational bases for Moufang, Bol and C-loops. We also
discuss the case when the inverses are only one-sided and/or the neutral
element is only one-sided.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat